Is it normal pus keeps coming out of my gum

I have pus that comes out of the gum behind my wisdom tooth but no actual fever or pain. Very occasionally little flecks of chalky white stuff come out with the pus.

The pus doesn't come out constantly, just when I squeeze the gum. There is normally a faint background taste of pus around that wisdom tooth though. I wouldn't want to try kissing anyone. This has been the case for about 4 weeks now. Dentist said it's not infected because there is no fever or pain, it's just inflamed, so it doesn't need antibiotics... she told me to have my wisdom teeth removed though.

Does pus come out of non-infected tissue??? I'm worried. I don't know whether to trust the dentist.