I hope your finger is getting better by now.

There is a general rule about hand bone swellings...

Distal joint (first joint from the finger nail) may develop hard lumps called Heberden's nodes. Normally these are supposed to be painless...but mine are not, esp when starting up.
This is typically thought to be osteoarthritis.

Swelling of the proximal knuckle joint ..at the metacarpal area can be sign of inflammatory arthritis. RA specifically.

I'd put some antibiotic ointment on that bite, just in case. Sometimes a bug can introduce staph that was already on the skin and push it into the bite....hence it may become infected.

Many years ago I was bitten on the eyelid by a black fly (these need blood to reproduce like mosquitos do). The bite itself was painless. Next day I developed a staph infection, and was very ill...high fever, swelling on that side of the face-- with the eye pushed shut. I drove 50 miles to the nearest hospital (this was in Maine), and was given erythromycin.

If anything gets worse with this thing on your hand, please see a doctor ASAP, Lara.