OP, I would very much recommend writing some bullet points or a note to your GP to help during your appointment if/when you go on Wednesday. I find sometimes I can intend to be completely open with professionals, then go in, feel silly and ridiculous because I'm 'quite clearly overreacting' and then play it all down (as I think you probably are with the purging) or come across as if all is fine and normal. Writing it down so it's there in front of you allows you to just hand it over if you feel 'silly' or nervous saying it.
I would also recommend asking for a blind weigh-in, as suggested above, if you're very uncomfortable about it. They are likely to ask to weigh you, but if it really comes down to it, let them know that you don't feel happy to be weighed there right now. The most important thing is to stop the purging/disordered behaviours (and the thoughts underlying those).
It sounds from what you have written so far (and the height/weight mentioned) that you're not actually 'binging' objectively, but more feeling uncomfortably full and bloated after 'normal' portions of 'heavier' types of food? I can relate to this also. Please do be very careful. You are not far off the anorexia nervosa weight criteria (and even that is more subjective now).
Things can deteriorate rapidly with disordered eating and health. My vital signs were borderline normal one week, and the next they were looking for a bed for me because my heartrate and BP dropped massively and my body stopping coping.
I don't mean this to all sound very clinical and 'dramatic'. But please do tell them honestly. I am a similar age - 27 - and have purged now for 11 years regularly. I didn't think I'd ever have an eating disorder. I didn't see it as a 'big deal', I wasn't noticably thin, I was just average, studying, working, socialising, fine, just purging after meals when I felt too full. I couldn't stop it, but I didn't need to, it was just normal, and no one had to know. I could justify it. And then I couldn't stop. And I started doing it more. And purging after any food. And then after tea. And then water. And then it wasn't enough so I stopped eating altogether. And exercised more. And tried everything else. And ended up in hospital for 5 months. It's really, really not worth that. And now, 3 years after that, I am still consumed by that every day, still thinking of nothing else and purging daily. You've done this for 8 years. Do you really want to be doing it still in another 8?
Please tell your GP and ask for a referral. I would also recommend the book Beating Your Eating Disorder. (www.amazon.co.uk/Beating-Your-Eating-Disorder-Cognitive-Behavioral/dp/0521739047/ref=sr_1_1?ie=UTF8&qid=1487029639&sr=8-1&keywords=beating+your+eating+disorder). Even if you don't feel you do have an ED yet, it's got useful sections to help you think about motivations and being ready to change behaviours, the way you think about food, all sorts.