There is no official townland called Brownsgove in Co. Galway. There is a Brownsville and a Barnwellsgrove. Possibly Brownsgrove is a local place name. I did check the subscription site Roots Ireland and there were 42 William Kelly baptismal records in Co. Galway from 1832-1842. Also, a good number of Galway RC parishes do not have records back to 1837.
Are you aware of any siblings?
Have you considered DNA testing?