I get excessive thirst from the Nortriptyline that is part of my med regime. The tricyclic antidepressants are notorious for that.

Always make sure that your doctor has ruled out diabetes, or another medical problem, before assuming that it's safe just to self treat.

There are oral rinses, like Biotene or Act, that can help oral dryness. Sucking on hard candy (regular or sugar free) can offer some relief.

Profuse sweating from RSD could contribute to dehydration and increased thirst, but I don't recall other posts here about excessive thirst because of RSD. I have seen many posts about dry mouth as a side effect of meds, like Bram and I.

Good luck figuring it out.