Not sure if you were able to find Elinore "Nellie" Welch from earlier post,
Sylvester Welch and Jemima Carroll have roots to Fauquier, Loudoun, Hampshire, Northumberland counties in Virginia. I am decended from Sylvester and Jemima's daughter Mary Welsh, who died young with four kids. The records primarily have Jemima and Sylvester up in Hampshire late in life. Mary's husband William Mott remarried and stayed in Fauquier, believed the children stayed in Hampshire Virginia with Sylvester. 1800 will probated in 1810 for Sylvester only indicate his imediate kids and the children of Mary. Again no mention of Nellie. There are a number of Welch families up in Loudoun/Fauquier on tithable lists.
In tracking back, found indications the Jemima line originated from Northumberland Shire in Virginia. Through Major John Welsh, his son Sylvester b. 1670
married an Elinor, and had a daughter Elinor Welch b1704, so the name was in the family.
1. Major John (b1622) - emagrated first around 1650, moved MD
2. Sylvester (b1670) - Anne Arundel County, MD married Eleanor?, daughter Eleanor
3. Sylvester (b 14 NOV 1696 in Northumberland)
4. Sylvester (b 01 OCT 1729 St Stephens, Northumberland VA m. Jemima Carroll
Had Pat Duncan do a lookup for me on Loudoun of Welch family and fair number of candidates there as well as Fauquier. Happy hunting.