Prozac was the very first medication they tried me on; I was on various dosages for about a month and a half for depression/anxiety and I did alright on 20 I mean it helped a little; but when he put me on 40 the depression/anxiety came back with a vengeance and I just felt worse on the 40's. So I switched to Effexor which was way way way worse.
I hope the prozac works for you; although I never tried it for binge eating. Good Luck I was on Vyvanse when I was a teenager for ADHD and I was never hungry on it; I would eat small meals; granted it could have been the fact I was active in sports and felt pressure to maintain the weight I was at that time.