
Questions & Answers about haguki ga haremashita.
が marks 歯茎 as the thing that underwent the change or state described by the verb.
In 歯茎が腫れました, the gums are the thing that swelled.
So the structure is basically:
- 歯茎 = gums
- が = subject marker
- 腫れました = swelled / became swollen
A natural English translation may use my gums as the subject, but Japanese often just states the body part directly.