Long ago I discovered Fordyce spots on my lips and spent months convinced I had warts. As far as I know, and I agree with veryworried, warts don't usually come on that intensely as well as tinily. I'd def go see a doctor but sounds like fordyce to me and you just over inspected and found something that's been there. In the case of lips at least, they can become more visible as we age so perhaps that is what is happening to you.
They don't sound like warts, but you should see a dermatologist asap and ask for one to be biopsied to know for sure what they are, assuming the doctor agrees it is worth investigating. Yes, they are typically bigger but the most frustrating thing about HPV is that there is no "typical". No definitive look for everyone, no idea how long they last for everyone, etc. Go see a doc.