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.
"Binging is a descent into a world where every restriction... is cut loose. At its core is a feeling of deprivation.. a feeling you can never get enough. Binges do not signify a lack of willpower or inability to care for yourself. On the contrary, binges are a urgent attempt to care for yourself when you feel uncared for. They are the voice of survival. Binges are the mark of the self that says, 'I am tired of feeling deprived, of being told I am wrong, that I am bad." - Geneen Roth