No it is not an infection, nevertheless I did some tests and it emerged that I had nothing at all.
I'm talking about my case, but I think it is the same for a lot of people here, I was used to pull my lips out constantly, of course, but there were not really lacks of blood and the vermillon is just a protection layer of the fleshy tissue which is armed with all the necessary tools to fight against whatever infection.
Then, if we had an infection, we would have more than just a proper peeling cycle. I have any kind of others problems at all. I have a respectable hygiene, a balanced diet, I don't drink alcohol, neither smoke at all, and I make sport.