A hemorrhoid is not an STI, and hemorrhoids are never a sign of one.
Are they sure it was a hemorrhoid? It's not impossible for that to become infected, but it's considered rare for that to happen. Perhaps the fingering caused a cut and that got infected? Hemorrhoids can need to be lanced, but being infected is rare.
In any case, fingering does not transmit STIs, and while unprotected oral can transmit them, none would cause anything that needs to be lanced.
Unprotected oral can transmit gonorrhea, chlamydia, syphilis and herpes - none of which would cause anything that needs lancing.
I'm sorry that happened and it sounds very painful. Make sure to follow their instructions so it doesn't get further infected.