Is my cartilage piercing infected?

Sorry to gross you out this fine morning/evening wherever the hell you are..
But this morning I noticed that one of my two cartilage piercings had a tiny little bump next to it, which I immediately recognised as a cyst.
I left it alone, and just now I noticed it had burst, it was really tiny, some white fluid (pus?) came out and I cleaned it up as best I could, it bled a tiny bit as well. It didn’t hurt at all, I wouldn’t even have noticed if I hadn’t looked in the mirror.

Also I was at the doctor this morning for something separate, and got antibiotics for my sinusitis (I feel like an OAP..), amoxicillin, for a week, would this also work in preventing/counteracting any infection in my cartilage? (If so a happy coincidence!)

I was told by people/ the piercer (AKA heavily tattooed lard arse) that I should soak it in sea salts and that small cysts are normal for up to 7 months afterwards as long as they dont get overly large or painful. The place was a bit dodgy though as I got it done with friends on a whim… alcohol was involved. So is this advice right? Or should I be worried.

Also heard that as a rule of thumb you NEVER take a piercing out of an infected ear.. something about it moving the infection deeper INTO the hole??

Slightly confused right now.. But should I do something? Doctor isn’t an option for another week or so.. but should I leave the earring in or not? Watch it and see if something bad happens???