[akstrohm]

It's most likely that you're allergic to the hay or bedding.

Fleece is the best bedding for allergies. If you're not familiar with it, read the Fleece Project sticky in the bedding section.

Kleenmama's bluegrass hay is one of the best for people with allergies. Otherwise get the least dusty hay you can find. You can put hay in brown paper bags ahead of time (or have someone else do it for you) and just put a bag in the cage when needed. This will cut down even more on dust.

I know you didn't mention this, but don't bathe your pigs too often (no more than once every 6 months). They're probably not the reason you have allergies, so bathing is unlikely to help, and it will only make their skin dry.