I don't know where you live but please DUMP this pediatrician immediately. Even if there were any reason to stop breastfeeding (and I don't see how there could be), the way she treated you was borderline abusive! Screaming, calling you (and us) crazy, shouting at you stop crying in her office? I would never see her again.
As for your son: If you are petite and your husband or SO is on the small side -- 5'7" is pretty short, my husband is 5'8" and people say he's short --has any doctor ever just realized that your son has "short genes"? Our godson was very, very small and up until he was about three, his parents were in constant panic that he was "failing to thrive" or not absorbing nutrients or something. Doctors bounced them from program to program, test to test, until ONE doctor actually looked at the parents. Dad is very short and very, very slim and eats like a horse but never gains an ounce. Mom is very short and heavier but still -- very short. Their son is perfectly healthy and is always going to be short and very slim! It was genetics, not some defect. Your son may indeed be as short as you are. Why would that be a problem if he is healthy?
Now, if you have hormonal issues your son may as well, so I think you're right to want to find an endocrinologist who will listen to you about your own family history and possibly test your son. At a minimum an endocrinologist should have asked to see your son again in a few months and consider then whether to test him, depending on his growth. But please consider that your son may just be a small person, period. Being small and being healthy are not mutually exclusive. He is eating a lot, from what you say, and is developing mentally and physically. I would find a better pediatrician, and see if that doctor is concerned about his weight or not. Then go from there.
A couple of things to bear in mind: You mention seeing "a series of pediatricians." That's kind of a red flag; I have to ask, do you think you might have been doctor-shopping in hopes of finding a doctor who is as concerned as you are, even if there is not a reason to be concerned? You seem very, very focused on whether your son will be short.You want him to be "happy, healthy and have every advantage iin life" but seem to be equating that, at least in part, with his weight and height. To be honest, you sound like you are anxious and perhaps too fixated on the size issue and on how that affects the entire rest of his life. You can't control whether he is going to be small but you can control your anxiety -- which he can detect, even at his young age; parental stress does telegraph itself even to young children.
Please think hard about whether you have other sources of anxiety and stress that might be manifesting themselves in this intense focus on his size. (IF he is otherwise healthy-- I am not downplaying your concerns, just noting that if doctors say he really is healthy, just small, the focus on size may indicate that you need something to focus on....)
In the country where you live, do you have any support system or family or friends other than your husband? It sounds like you could use a reality check with some experienced moms or just some time away from your son with other adults. I worry that maybe you are focusing in on him like this possibly too much and it's a focus for a more generalized anxiety or stress--? Just something to keep in mind.