K.C.
The same thing happens to me every few months but more so with my engagement ring than my wedding band. When it's just my engagement ring I just take it off for a few days until it heals. When it gets really bad I take them both off and wear my wedding band on my right hand instead. When I was fat and pregnant I actually wore them both on my necklace because my fingers were so swollen they wouldn't fit. Anyway, I've found that Eucerin cream works well to heal the chafing and it only takes a few days. My problem is the amount of time my hands spend in water and then not fully drying or letting air get underneath the rings.
Good luck and congratulations with you new babies!!!
K. - SAHM of 2 boys