John may have had a brother James. 
The James Barrett mentioned above as a possible brother came in 1635 to Massachusetts and settled in Malden. He also was at Charlestown. He died 08-16-1672. He married Hannah Fosdick daughter Stephen, she died ca1615 died 1681 she m2.John Scolley. James and Hannah had: James born 04-06-1644, Hannah born 03-21-1648, Mary, Sarah, John born 05-06-1655 and Stephen. 
John Barrett of Chelmsford by wife Susan had Lydia born 1659 and Samuel born 06-16-1660. 
See https://ancestors.familysearch.org/en/LZR1-B1R/john-barrett-1635-1711, its information is a bit off from what was previously known about John Barrett, including her maiden name. It does give his parents as Humphrey and Mary (Hawes). Humphrey Barrett born 1592 England died 11-02-1662 age 70, came about 1640 to Concord and had 300 acres and house on lot #12 which is now Monument Street in Concord, freeman 05-06-1657, moved to Marlborough, married Mary ____ born c1590 England died 1663 age 73, will dt.06-15-1663 pbt.10-20-1663, names sons John and Humphrey and grandchild Mary B. also her brother Oliver who died 09-__-1671, 4 kids, all born England: 
- Thomas drowned in the Concord River in 1652, widow Elizabeth  ? m2.Edward Wright, son Oliver died 1671 
- Humphrey, of Concord, born 1630 died 01-03-1715/6, freeman 1682, rep.1691, m1.07-17-1661 Elizabeth Paine she died 1674 1 child: Mary married Josiah Blood, m2.03-23-1764/5 Mary Potter she died 11-13-1713, she daughter of Luke Potter an early Concord settler, 2 kids: Capt. Joseph born 1678 died 04-04-1763 married 1701 Rebecca Minott died 06-23-1737, and, Benjamin born 05-07-1681 Concord died 10-25-1728 married 01-03-1705 Lydia Minott, sister of Rebecca, 8 kids: Benjamin (died 10-23-1738 Concord and had Benjamin, Jonas and Rebecca), Thomas, James, Lydia, Thomas, Mary, Stephen and Rebecca. [This would seem to prove that Humphrey Barrett Jr. is not the father of ancestor Benjamin Barrett as Humphrey's son Benjamin did not have a son named Isaac.] 
- John of Marlborough 
- James of Charlestown 
Richard Barrett died 1651 married Elizabeth  ? of ?Lynn Massachusetts. Richard Barrett died 1651 married Mary ____ of Boston, 1st child born 1658, or ?1641. 
Robert Barrett died 1675  married Hannah Carter born 1640 died 1691 of Charlestown, 1st child born 1663. 
Walter Barrett of Cambridge (Middlesex) Massachusetts by wife Sarah Champey, daughter Robert, had Lydia, John born 1660. 
By 1657 there were four immigrants named Barrett in New England. These were: Humphrey to Concord 1640, Samuel to Bedford 1656, Thomas to Braintree 1645 and to Chelmsford 1663, and, William to Cambridge 1656.

Historical
1620-1621: Poland, Turkey - Polish-Ottoman War over Moldavia
1620: Poland - Battle of White Mountain, Emperor Ferdinand II, Holy Roman Emperor, defeats the Bohemian rebels
1620: Romania, Turkey - Bethlen Gabor allies with the Ottomans and an Invasion of Moldavia takes place, the Polish suffer a disaster at Cecora on the River Prut
1620: United States - The Puritan Pilgrims arrive in the Mayflower at Cape Cod
1621: Poland, Turkey - The Battle of Chocim Poles and Cossacks under Jan Karol Chodkiewicz defeat the Ottomans
1621: United States - The Pilgrims celebrate the first Thanksgiving with their Indian neighbors
1622: United States - Jamestown massacre Algonquian natives kill 347 English settlers outside Jamestown, Virginia (a third of the population of the colony) and burn the Henricus settlement
1623: Italy - Maffeo Barberini is elected Pope Urban VIII at the Papal conclave of 1623
1624-1642: France - As chief minister, Cardinal Richelieu centralises power in France
1625: United States - New Amsterdam founded by the Dutch West India Company in North America
1626: Italy - St. Peters Basilica in the Vatican completed
1626: United States - The Dutch buy Manhattan Island for $24, a presence is established but no large settlements made
1627: France - Cardinal Richelieu lays siege to Protestant La Rochelle which eventually capitulates
1629: France - Cardinal Richelieu allies with Swedish Protestant forces in the Thirty Years War to counter expansion by Ferdinand II
1631: Italy - Mount Vesuvius erupts near Naples
1632: germany - Battle of Lutzen (first of two), death of king of Sweden Gustav II Adolf
1633: Italy - Galileo Galilei arrives in Rome for his trial before the Inquisition
1633: United States - The city of Baltimore is settled
1634: Ethiopia - Emperor Fasilides expels the Catholic Patriarch Afonso Mendes and several Jesuit missionaries from Ethiopia
1634: Germany - Battle of Nordlingen (first of two), in Bavaria, results in Catholic victory
1636: Ethiopia - Emperor Fasilides founds the city of Gondar, which becomes the capital of Ethiopia for the next two centuries
1636: United States - Harvard University is founded in Cambridge, Massachusetts
1636: United States - Roger Williams is driven from Puritan Massachusetts and settles Rhode Island, a haven for religious freedom
1638: United States - Delaware is settled by Peter Minuet
1639-1651: England, Ireland, Scotland - Wars of the Three Kingdoms, civil wars throughout Scotland, Ireland, and England
1639: Italy - Disagreements between the Farnese and Barberini Pope Urban VIII escalate into the Wars of Castro and last until 1649
1639: Spain, England - Naval Battle of the Downs, Republic of the United Provinces fleet decisively defeats a Spanish fleet in English waters
1639: United States - John Wheelwright is banished from Boston and founds a colony in New Hampshire
1640-1668: Portugal - The Portuguese Restoration War led to the end of the Iberian Union
1640: England - Torture is outlawed in England
1640: Scotland - King Charles was compelled to summon Parliament due to the revolt of the Scots
1640: United States - The population of the American Colonies is estimated at 5,700. Starting in the 1990's, Charles Anderson of the New England Historic Genealogical Society begins books that provides information about all persons in New England by 1640.
1641: France - Rene Descartes publishes Meditationes de prima philosophia Meditations on First Philosophy
1641: Ireland - The Irish Rebellion
1641: Japan - The Tokugawa Shogunate Institutes Sakoku, foreigners are expelled and no one is allowed to enter or leave Japan
1642-1649: England - Civil War in England, Charles I is beheaded by Cromwell
1642: England - Isaac Newton is born
1642: Neatherlands, New Zealand - Dutch explorer Abel Janszoon Tasman achieves the first recorded European sighting of New Zealand
1644-1674: Mauritania - The Mauritanian Thirty-Year War
1644: China - The Manchu conquer China ending the Ming Dynasty, the subsequent Qing Dynasty rules until 1912
1644: Italy - Giovanni Battista Pamphili is elected Pope Innocent X at the Papal conclave of 1644
1645-1669: Turkey, Italy - Ottoman war with Venice, the Ottomans Invade Crete and capture Canea
1645: Japan - The death of Miyamoto Musashi, legendary Japanese Samurai warrior of natural causes
1647-1652: Spain - The Great Plague of Seville
1647: Turkey - Seven-year-old Mehmed IV becomes Ottoman sultan
1648-1653: France - Fronde civil war in France
1648-1667: Poland, Lithuania - The Deluge wars leave Polish-Lithuanian Commonwealth in ruins
1648-1669: Turkey, Italy - The Ottomans capture Crete from the Venetians after the Siege of Candia
1648: Spain, Italy - The Peace of Westphalia ends the Thirty Years War and the Eighty Years War and marks the ends of Spain and the Holy Roman Empire as major European powers
1649-1653: Ireland - The Cromwellian conquest of Ireland
1650: United States - An estimated 40,000 people are living in the American Colonies
1652: England, Netherlands - Anglo-Dutch Wars begin
1652: South Africa - Cape Town founded by the Dutch East India Company in South Africa
1654-1661: Turkey, Albania - Mehmed Koprulu is Grand Vizier
1655-1661: Sweden - The Northern Wars cement the rise of Sweden as a Great Power
1658: India - After his father Shah Jahan completes the Taj Mahal, his son Aurangzeb deposes him as ruler of the Mughal Empire
1660: England - Royal Society of London for the Improvement of Natural Knowledge founded
1660: England - The Commonwealth of England ends and the monarchy is brought back during the English Restoration
1661: China - The reign of the Kangxi Emperor of China begins
1661: India - Mehmed Koprulu dies and is succeeded by his son Ahmed
1662: France - Jacques Aymar-Vernay, who later reintroduced Dowsing into popular use in Europe, is born
1663: France - France takes full political and military control over Its colonial possessions in New France, microscope of Hooke discovers cells
1663: Turkey, Austria-Hungary - Ottoman war against Habsburg Hungary
1664: England - Forestry book by John Evelyn called Sylva is published in England
1664: Hungary, Turkey - Battle of St. Gotthard (first of two), count Raimondo Montecuccoli defeats the Ottomans, the Peace of Vasvar is Intended to keep the peace for twenty years
1664: United States - British troops capture New Amsterdam and rename It New York