Yes, OP can draw out an infection. This has been posted many many times. Have you thought about Oil of Oregano instead of the peppermint? It's a powerful antibiotic. Use for 10 days only though, just like an antibiotic.
Just think about it. If you had that infection lingering in your gums, most likely you were introducing it to the rest of your system, without even knowing you were doing so. That heavy duty bacteria could cause so many other problems systemically.
Now you are pulling it out and spitting out the bacteria.
All I can say is....good for you!!
I know others on here that have had infections, and I'm hoping they will come around and talk about their experiences as well.