Hi Kate,
Just for your information, my 2nd great-grandfather was a James Burrell born 1834 and he married an Elizabeth Carter in the Shankhill Parish Church, Lurgan on 15 June 1857. His father was William too and I believe he was a brother of your ancestor William born 1838. There was also a Thomas Burrell born in 1839, another son of William snr's, who got married in the Shankhill Church.
My great-grandfather (James's son) was also named William and he called 3 of his sons William, James and Thomas.
Regards
Russell M