It could be a yeast infection. Those can be treated with over-the-counter medications, which is the first thing I'd try in your situation because of the hassle of going to a doctor. Can you tell your mom you think you have one? (Yeast infections can happen to anyone, it doesn't have to do with having sex.) She can take you to pick up a medication, or she might just buy one for you.
If the dots and itching don't resolve with treatment, go to see a doctor or preferably an ob/gyn and have it looked at. (But nine chances out of ten it's just a yeast infection.) As for the wrinkly skin, that could be normal. If you do go to an ob/gyn, you could ask.
I agree that yeast can look that way but if you are looking close up with a mirror and aren't having any issues like itching or burning that our skin can just look a little funky there like that. The surface is often not completely smooth. At 13, you may be able to talk to your doctor about it with or without a parent in the room to find out if this is normal. Unless you are having other symptoms, I'd guess it is normal.
If it were just little bumps, that does sound like it could be normal, but she said it had itching and little white spots, which to me sound a bit like thrush. That can be treated with either clotrimazole (which is available over-the-counter) or by prescription meds. It seemed simplest to try the otc approach first and see if things improve.