Hello marcie
On a parent search through IGI, I can see two possible births to a William O'May and Margaret Milloy. These being a Catherine Taylor O'May on 30/1/1863 in Campbeltown and an Alexander O'May on 13th June 1860, also at Campbeltown.
If this is the same family and assuming the parents married pre 1860, have you checked scotlandspeople for marriage certificate and/or death certificate for William, as either should (assuming marriage after 1854) give his parents names, which in turn could help with finding him in Ireland. Or, if he and Margaret actually married in Ireland , the birth certificates of their children born in Scotland, should indicate when/where they married, which could also aid your research.