You might find that it's not mites. I have quite bad hayfever, with allergies to a range of different pollens and grasses. If my arms, neck or hands come into contact with hay I come up in tiny, itchy red welts...as I found out the first time I climbed into the hayloft at a riding stables!
If it's hay from a new place, you may find that it's a different type of hay to the one you were using before, hence the allergy.
If you're safe to, you could try some over the counter allergy tablets to see if this helps at all. If it seems you are allergic, the best thing you can do is keep covered when coming into contact with the hay (and unfortunately the pigs for a while, until you go back to a hay to which you don't react)