Welcome and thanks for posting your query to HCM.
after reading your query, we can make out that your problem is related to simple trauma/ injury
to the labial skin. You know very well that after every type of injury we do have inflammation and swelling of skin and the same thing happened with you. Due to friction and trauma during intercourse you had injury on right labial skin. Your birth control device has nothing to do with this swelling. So don't get panicky about the same.
The problem will be alright in couple of days. In between take a good pain killer tablet after meals according to pain status and can do cold
compression over the area to reduce the swelling.
With best health wishes,
Dr Sanjay K Kanodia
MD ( Dermatology and STD/ Venereology)