Suellen:
I searched Roots Ireland for a Mary Welch from 1823-1833 in Co. Galway and there were 50 baptismal records, all had the surname Walsh. I then added father John and mother Mary and was down to one record an 1827 record in Tuam. However, there was no companion record for an Ellen Walsh for those parents so I don't think that is the correct family.
Some churches in Co. Galway don't have records back to the late 1820s so possibly your family belonged to one of those churches.
Roger McDonnell