S2S,
I have had the kind of cyst you have mentioned, and also a few cysts on the inside of my bottom lip. I believe they're caused by blocked saliva glands. The tear is possibly related to the cyst trying to excise itself.
Rimming is the red herring here and is not even something you need to mention to your GP. That said, they've seen and heard it all before anyway.Just go see a doctor.