Same happened to me. Swollen right side of the penis after having sex two times with my wife, without removing the nuvaring. It doesn't hurt and it isn't irritated, just size increased, like irritated ganglions. Now I'm worried about cancer and if it doesn't go away in 5 days, I'll go check it ... :((
Hello,
It can be due to friction rub or chafing with the nuva ring or due to allergic reaction to the Nuvaring or the vaginal lubricant if you are using any. Use a water based lubricant like KY jelly or indulge in plenty of foreplay so that there are less chances of an allergic reaction.
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.