This is very common my daughter gets it she simply put a cream on it it is one of the cortisone creams, google it , it is an allergy to the ring materials my daughters ring is yellow gold and she gets it also with gold earings, behind her ears.
Thanks for the post.
I know it sounds very strange that the ring causes allergy on one finger but not on the other. However it is possible to have localized allergy to a particular metal. Alternatively maybe you had a very mild allergy, hardly noticeable, on that finger that got aggravated by gold touching it.
I would suggest you see a skin specialist to know what it is exactly. If it was only due to localized reaction to gold, it should have healed by now.
Hope this helps. Please let me know if there is any thing else and do keep me posted.