If you continued to drink while on Prozac, you didn't really give it a fair shot. People shouldn't drink while on antidepressants, according to manufacturer directions. If you are looking for the solution to quitting drinking in a pill, I'm afraid you will be disappointed.
It's true that a small percentage of people gain weight on Paxil, but that does not mean you will...so be careful about how much you eat and exercise, and you will probably be all right.
I agree about the prozac. I know I shouldn't because it has perhaps helped a large number of people but ... I am wary about all psychotropic medications and when I was in hospital it was mandatory to take it for six weeks (some govt./ health policy).
I'm not sure about weight gain.
A similar question has been asked before but I think in relation to a different drug. If you had the time and were impatient for a response you could always try doing a search. This other person was afraid of weight gain due to BDD. I don't know if that helps.
J