That's super common, it's from your rats' sharp little nails. Some people are more sensitive to it than others- I basically can't touch my rats with bare skin anymore or I get huge welts that last for hours. That's an unusual reaction on my part though, most people only have minor irritation that goes away quickly.
You can trim their nails yourself with clippers or a dremel, or provide rough surfaces like lava ledges, bricks, and concrete (check garden stores to see if they have broken pieces you can have for cheap/free) for them to walk over and wear down their nails themselves. For best results put the stone right underneath their water bottle so they have to stand on it daily. If they use a wheel, some people put sandpaper inside the track but others feel that's too harsh.
Wearing long sleeves will also help prevent them from getting their nails into your skin in the first place.
As for the rash, wash your skin after you let them climb on you and if it's really bad or itchy, take an allergy pill. Topical sprays and lotions will also help, I have had good luck with Benadryl spray but not so much calamine.