Not to overstate the obvious but binge eating is a psychological issue - you say you don't have any psychological problems that you know of but then you eat until you are about to explode with no explanation - there is no physical justification for this, it is psychological, so go see a doc like you suggested and get it sorted out.
I used to binge eat a bit and found that it was linked to some depression. I changed my habits over time but it takes a lot of work and time and if you have someone that can assist you with that I say go for it. It will only get worse if you don't address it now. Good luck!
One thing you can do for yourself is right when you get the urge to binge eat stop and ask yourself what you are thinking/feeling at that moment. Lots of times the emotions that trigger the eating disappear immediately during and after the eating so identifying how you feel right beforehand can really shed some light on the situation.