It's ok to tell your doctor about your binge eating, but what are you expecting he'll do? Best case scenario he'll refer you to a psychologist. Worst case scenario he'll tell you to go on a diet. Either way, he's not the one who is going to help you out of this. In my experience doctors don't know much about anything outside of what they specialize in. I might be pessimistic but i've had some bad experiences with doctors. If you are to tell him, do so specifically to ask for a referral. Instead of saying "I have a problem with binge eating, what should I do?" say "I think I suffer from an eating disorder, is there a therapist you can refer me to that specializes in eating disorders?" I hesitate because there are even some doctors who don't believe that binge eating is an eating disorder so just be on the lookout if you doctor isn't being sympathetic with you. If he starts talking about dieting, eliminating certain foods etc then you know he just doesn't get it so be prepared for that.
“If you try to lose weight by shaming, depriving and fearing yourself, you will end up shamed, deprived, and afraid.” Geneen Roth