Can you post a photo of the lip are?
First identify it is swollen. Sometimes retained lip scales will make them look that way.
Here is a photo of my girl Lucky. If you look at her upper lip you can see the slight swollen area.
Treatment from my vet. consisted of poking the lip area with a sterile needle. According to him it releases the infection by causing it to bleed.
It worked great and she only had a small scar from the procedure.
I use the same practice on the Ranch. I use a needle on a diabetic syringe. They are cheap and work great.
The second photo shows the lip still out but that is from the scar tissue.