After I eat I get a tickle sensation on the rt side of throat. Feel like I want to cough but I don't. Don't get it when I drink fluids.?

Tonsils? I'm guessing you have some kind of irritation in your tonsil or your throat. Maybe even a tonsillith. The only way to be sure would be to have an ear nose and throat doctor take a look. There are other reasons for a throat tickle, like a swollen thyroid gland or an injured nerve. But those are less common.