There is an Aaron Kelly age 14 in the 1871 census living in Patrick - possibly the same one as found in 1881. Unfortunately his mother is listed as Isabella.

Patrick, Ballaquayle, RG10/5771
Isabella Kelly, Head, Wid, 58, b.Malew
Aaron Kelly, Son, 14, Carder (wool), b.Patrick

I believe the same Isabella is to be found in the 1881 census (familysearch.org) living on her own in Patrick.

Isabella KELLY, Head, W, 66, b.Malew, Miners Widow

The only other Aarons I can find on the island in 1871 are:

Aaron Mylchreest, 10, b.Patrick, living Patrick
Noble Aaron Senogles, 7, b.IOM, living Lonan
Aaron Wade, 3, b.German, living German

Regards,
Ruth