Allergies are such a mystery!! I have worked for two different allergists, and we've seen some strange things. It could be almost anything. It could also be a cross reaction between two seemingly non-related things. We had a patient break out in hives from eye drops and a neosporin product- cross reaction. You may be able to eliminate certain things and figure out a culprit, but the allergist will be able to help you out in narrowing things down. Typically, but not always, a food allergy will start at the point of entry, so if it's something she ate, her lips/face would swell first.
I would also be sceptical that brand new hives would show up on the back from the ibuprofen reaction. But, like I said, you can never say never with allergies!! I doesn't matter if you have used things before, they cause a reaction after at least one exposure. So, when people say they've eaten shellfish for years.....well, the allergy will show up AFTER they've eaten shellfish, not the first time.
Personally, we've had our own craziness - my daughter reacted to an antibiotic eye drop after treatment for pink eye. The pediatrician said it was HIGHLY unlikely her hives were from the eye drop. I asked my allergist and he said it sure could. It's not common, but possible. When my oldest was a toddler, he would break out in hives for no reason, on top of his allergy to dogs. I requested an epipen for my own reassurance. NEver had to use it, and he outgrew all of the allergies and idiopathic urticaria, but I was happy to know that if he had a bad reaction, I would be prepared.
Also a word of warning- the last round of hives may not have a obvious source. Sometimes, especially in children, hives just come for no apparent reason. The allergist can test for all the inhalants, foods, etc and there may not be an answer. This happens frequently, too. There are a couple ways to test (skin testing and RAST tests) RAST tests aren't as reliable as the old-fashioned skin testing, but for kids- an alternative.
Good luck at the allergist - I hope y'all can find a cause.