I'd check for allergies just to be on the safe side as well BUT, typically, an allergic reaction wouldn't go away on it's own after 10 minutes, so that may not be an issue here. My daughter had an interesting allergic scare last spring that turned out to be an overwhelming immune response and not allergies, but I learned a lot about allergies in the process. One night, we had dinner, nothing happened. Next night we had leftovers and the following morning, she was covered in hives. I took her to the Dr. who thought it might be an immune response to something and we ate the same leftovers again that night...about 30 minutes later I was giving her a bath and the area around her mouth started to swell and get red, this progressed up her cheeks and pretty soon her whole face was swollen. It scared me to DEATH!
Kids can eat foods repeatedly and then suddenly have allergic reactions one day to them. According to our allergist, you can be exposed to an allergen once and nothing might happen, a second time and get a bigger reaction, and a third time might be serious. Doesn't always happen that way but he was trying to explain what he initially thought was happening with our daughter.
Think about the ingredients of both the cake and frosting. Possible allergens include:
Milk (butter cream frosting)
Corn (corn syrup)
An allergist can run a basic panel that contains all of these for you just to make sure. It's good for peace of mind. We did a skin test on my daughter for all of those that I listed plus a few others at my request (dill, strawberries, oranges, several types of fish) because they were things she'd eaten around the time that her reaction happened, and they all came out negative. The answer for us is that our daughter had one cold after another thanks to daycare and her body's immune system over-reacted to something.
Also worth noting, they typically do not test for allergies until at least age 2 because they get a lot of false negatives until around then.
Hope this helps, good luck!