Hi Amy and Welcome to the Allergy and Asthma Forum!
I'm so sorry to hear about your little boy. Asthma is not much fun - especially dealing with it as a youngster. Both of my children had asthma since they were little, too (along with me), so I can understand your concern.
Re the bump on the eyelid...basically, after trying to research this I keep coming back to the same things. Styes. There are a couple of other things, but there's no mention of a 'hive'. I'm not sure why it turns up with his asthma. It could be a coincidence? Do you know what he's allergic to?
My suggestion to you, would be to bring him to an eye Dr. during one of these incidents, or his pediatrician. That will be the only real way this will get solved.
My best wishes to you and your son!! Let me know what happens, okay?
This link is to a discussion on 'eyelid bumps'.