my cat urinates every 10 minutes or so (kind of long)...

My cat, Aries, is three and 1/2 years old. He weighs 19 lbs, but he is just a big cat... he really is not that over weight (when he stands he reaches my waist with his paws), although he could loose one or two pounds (its hard to go on a diet for one cat when you have two).
Three months ago he urinated on my bed which is something he has never done before (he has always urinated in the ltter box). I noticed he whined when I put pressure on his belly so I took him to the vet. She said that he had some mineral build up in his bladder (she suspected) and after x-rays and the works she said he was o.k. she gave me some pills to give to him (not sure what they were-- one I think was an antibiotic). She said it was not a bladder infection. Ever since then, he's been urinating in miscelanious places around the house, and he goes to the litter box every 10 to 30 minutes. He usulally urinates a very small amount every time, but it's clear that something is wrong.
This is the second time he has been "seriously" ill and both times the vet could not find what was wrong. The vet is an extremely reputable place (VCA cat hospital of Philadelphia). Basically I can't afford another vet bill when the vet is not helping my cat. Has anyone experienced this before? Any ideas what could be wrong with my kitty?
By the way his brother has NO health problems whatsoever, so I do not think it is a parasite or anything like that...

Thanks for any help you can give me.

-Matt