I have, shall we say, a few skin issues that I've had looked into. Here's my experience.
Your general physician is most likely going to refer you to a dermatologist. Skin is complex. To give you an example. I have a persistent, random itch on my left side some nights, generally in the same spot. I'll feel an itch like I've been bitten, look down, see what kinda looks like a mosquito bite, that will get puffy and have very distinct edges....and then 15 minutes later it's gone. Fuckin' weird, right? Like my skin randomly deciding it's going to have a minor, localized allergic reaction. And yes, skin can respond to stress factors easily. I had a coworker I watched break out in hives during a really stressful situation for them.
The point is, how people's skin behaves is very closely tied to their genetics and there's a lot of things your skin can do (quite quickly actually) based on your genetics or other factors. So the answer of "what do these weird bumps that come out of nowhere come from" may be hard for them to speak to.
So what they'll want to do is biopsy one of these things, if they're able, to evaluate it. Skin growths can be lots of different kinds of cells. Not all of them are malignant.
A biopsy is usually done with an injection of a local anesthetic, so you don't feel them shave off and/or clip off a layer of skin. It leaves a pretty good scar depending on how they're doing it, and how much they need to sample. Average size of the area is like the eraser head of a pencil.
That may not even be necessary. Your doctor may have a better explanation of some special cells in the skin that can do weird, random things sometimes. But if you really wanna know, because it's not so major that you immediately sought a physician's opinion, they will all say the same thing "I can't tell you for sure just by looking at it." Whatever you're worried about has to be separated from you so it can studied, and I feel like that's worth letting you know about upfront. As a teen when I wanted to know about a permanent skin condition I have, it took a biopsy. (Which I never heard back about. Thanks, Dermatology.) As an adult who likes their time in the sun, I have some spots I wanted checked out. Also took biopsies. It's one of those things that doesn't occur to you at the time is a necessary part of finding out, but it is.
And don't be surprised if you get a shrug or a "that's very interesting...." because skin, complexion and skin reactions are actually pretty complicated. My brother has crazy reactive skin, to the point has to use steroid creams regularly to get his skin to calm down. I don't have his issues, but I have permanent marks on my skin where he doesn't.
Kinda sucks I know. I hope they have an easy answer that puts you at ease. But my general experience with dermatology is that they don't have a lot of answers for chronic skin stuff. They'll suggest it's something environmental you could try changing, because that is way cheaper and easier to try for the patient than biopsy. And a biopsy may tell them what it is but not why it happens.
Anyways, at the end of the day skin is weird and does its own things sometimes, including grow stuff. I wouldn't let it upset you too much, because part of dermatology thrives on people's insecurities about their looks. If they've burst and bled on their own though, yeah, that's something I would probably get checked out.
Re-reading your description, you might be dealing with
Skin Tags. Which are just one of the many odd things your skin can do.