It sounds like she has reflux brought about by the throw up virus she had. My daughter went through the same thing recently. I'm not sure why it happens, something about stomach acids and foods that produce more acid.
If your daughter is eating any acid producing foods, like tomato products or citrus fruits, it can aggravate the stomach and produce more acids which can cause the random throwing up and burning in her throat. With my daughter, we just took her off all tomato products and citrus for a week and she got better. My nephew had the same thing (he's the one who clued us in about our daughter), but he had to go on zantac before his cleared up all the way.
As far as the hives..... yuck! Two of my kids went through that a couple of summers ago (each a month apart) and it freaked me out! I don't do mystery illnesses very well!!! It was crazy weird, I have NO idea what caused it, and at the ER, they said it was probably a "virus." So, sorry I don't have a better answer for that, but you're not alone. If it helps, neither of them have ever had it again.
Anyway, so try eliminating all acidic foods from your daughter's diet and see if that helps.