S.B.
Congratulations on your new baby son!!!
I ALWAYS get a rash from hospital bands if they have to be on me more than a day. I don't know that I'm necessarily allergic to the bands themselves, but I think it has to do with getting sweaty under the bands and the skin not being able to breathe underneath. During extended hospitalizations, I have them switch wrists to give my poor wrists a break.
I usually use some anti-itch hydrocortisone cream. Since you have a new baby, you'll be washing your hands a lot. Make sure your wrists get nice and dry, but don't irritate the rash. You can use your blow dryer on a cool setting to make sure to remove the dampness.
You can always call the nurses station where you gave birth and let them know about the rash. They could tell you if you need to run it by your doctor.
Like I said, this happens to me every time and although it's very uncomfortable, it's never been anything serious.
Very best wishes to you!