Hello,
From the symptoms it can be contact dermatitis or allergic reaction. You should also maintain hygiene and try to keep the area clean and dry. Also use an antibacterial soap or mild soap like dove. You can also use a barrier cream with zinc oxide paste or calamine lotion or a mild steroid cream like dermacort on the rash. For the itchiness, you can take some antihistaminic like Benadryl or Claritin.
if the symptoms persist then please get an evaluation done from a dermatologist.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
sounds like you were either cleaning with something that got under your ring and irritated your skin under there... thats happened to me when i cleaned with bleach... just keep the ring off for now make sure you clean it before putting it back on... and just watch your hand to make sure you didnt touch or get into something your allergic to! hope this helps!