Does your doctor suspect hypoglycemia?
Pregnancy can cause hypoglycemia symptoms which should clear up in time. Having a baby can cause many temporary problems for mothers, I'm surprised your doctor has said only diabetes or HIV! Wow.
Some mothers do become type 2 diabetic during pregnancy so it is a possibility, and if you're eating a lot of sugar you will feel rotten!
Yes reactive hypoglycemia and weight gain are linked if your diet isn't under control. Excess sugar will be stored quickly by the over production of insulin, usually meaning weight gain. You should stop eating sugar and clean up your diet, regardless of what's wrong this will benefit you.
It may be that you're looking at diabetes rather than hypoglycemia. 1/2 hour after eating is when your blood sugar will be rising, producing a massive head ache and fatigue if your blood sugar is too high. You may also find that you're thirsty but not everyone experiences all of the symptoms. With hypoglycemia your symptoms of feeling faint etc would occur a bit later, between 2 and 4 hours after eating.
Let's see what your GTT results are. To me it sounds like diabetes is a possibility. If your doctor is unhelpful after the GTT then maybe think about seeing a different one - those absesses need seeing to properly.
You could also cross post this in the pregnancy part of the forum, maybe other mothers have experienced similar things