Any doctors out there?

So on Monday my cat bit the shit out of my finger and it immediately turned red, swollen, and painful. I didnt think much of it because that seemed like it’d be normal because there were two incisions on either side of my finger so I stopped the bleeding and washed it with warm water and antibacterial soap before bandaging it up. Flash forward to Tuesday my finger is throbbing and still red and swollen so I go into work and let them know that I can’t stay because I need to go to the ER and see a doctor about my finger which they were fine with. So I get to the ER and a nurse checks my finger out right away but then I’m stuck waiting for a total of 4 hours between seeing a nurse, being taken back into a different wing and sat on a bed in the hallway until the doctor can see me (all he does is check it out, tell me that it’s likely already infected, that it’s totally possible that the cats tooth hit bone and cracked it and then ordered an X-ray), then continuing to wait until I can get the X-ray, then again back to waiting while they look everything over and finally come back to me and give me a prescription for antibiotics and tell me to come back if A) swelling doesn’t go down within a couple days and B) If puss starts coming out of it.

Today (Friday) one side of my finger has started healing pretty well but the other side... not so much. It’s still swollen and hurts a bit when I touch the underside between the bites and is sore everywhere else on the finger. Also when I took the bandaid off this morning before cleaning, putting antibacterial ointment on it and re-bandaging it, it bled a little. Should I go back into the ER today? Or does it look like the bad side is starting to try to heal?

What I wiped off the bad side:

The bad side:

The side that’s closing up and healing a bit: