Slater's directory of 1846 is available online, but Glin is quite a small town and I dont see a listing for it. The nearest town to Glin that I see listed is Tarbert, which is in Co. Kerry. Link -
Slater's directory 1846 There are some Medical listings in Thom's directory of 1848, and the section for medical practitioners of the Coombe Lying in Hospital includes a Thomas Parkinson, with no other details.
The listings of Apothecaries Hall's (also in the medical directory) includes another possible listing for him as 'T. Parkinson, M.D. (Glasg), M.R.C.S.L., Broadford'. Broadford is also in Co. Limerick and about 45 km south of Glin.
You would need to establish the family religion to check for a baptism in parish records.
Shane