T.C.
Hi S.!
I second the cold... also I would try to elevate it as much as possible just like you would with a sprain or other injury. You need to be very careful trying to get it off though so you do not injure your finger to cause further swelling though.
When I swelled up during my pregnancy my Dr told me to drink more water. Did not make any sense to me but it did help relieve some of it but my toes and fingers still looks like sausages but my ankles went down a TINY bit- maybe it will help?!?!?!
Also, call where you got your rings from. They may have some suggestions. My girlfriend just had the same problem and while she had no choice but to have her rings all cut off they are fixing the ones that were purchased through them for no cost.
I really wish you lots of luck! Blessings to you and yours!