Same happened to me. If the rash is bothering you, you can do what I did. I put lavender and peppermint oil all around my finger. & it went away the next day.
I then went to kohls and bought new rings but before wearing them I put clear fingernail polish on the insides of the rings and haven't noticed a rash. But now 2 months later these rings are getting too small too :( I'm almost 37 weeks so I think I'm just going to go without rings from here on out.
I had the same problem when pregnant with my first. I'm almost 20wks and upto now still wearing my rings. I know I may have to take them off at some point but it won't be for long :)
I cried taking mine off. I didn't swell with my first so this time around made me really upset but i know after baby comes i can put them on again.
That happened to me my last pregnancy. I have a platinum wedding set we got me a yellow gold band to wear and the rash went away. Maybe just try a different metal in a bigger size if able.
I had a lot of swelling with my first two so I had to take mine off as well and wear them around my neck on a chain...it's normal don't fret