Problems effecting the lips are often troublesome and indeed hard to diagnose. However, such problems are rarely caused by STD's of any sort. if this were herpes or syphillis or any other STD that could be aquired through the oral tract believe me you'd know about it from very visable indicators- not a swollen lip. Also these would not occur on a 'every few days' basis.
This most likely sounds like a foreign body infection - i.e. an allergic reaction. The only real suggestion is that you go to the doctors where they can do a highly sensitive blood based allergy test which will diagnose the cause.
Well it is not an STD so you don't need any STD blood tests. Other then that it would be best advised to see a Dr before tests to see what he/she thinks. Best to go when the lip is swollen.