How to get rid of blackheads & bumps, and whiteheads?? Can someone please answer this question?

My skin is almost perfectly clear besides a few small bumps on my forehead, this one small blackhead on my cheek, and a whitehead under my nose. It's really frustrating because I really want clear skin. The bumps aren't as hard to clear as the blackhead. It NEVER goes away no matter what I do. The moisturizer I use doesn't work, and neither does my face cleanser. My stepmom told me to 'scratch' it away, which is the same as popping it, and I know you're never supposed to do that because it can leave permanent acne scars. But she really wants me too, she said if I don't I can get a crater on my face...I don't know if that's true or not but I really do NOT want that. 1: What can I do to get rid of the one blackhead? And I don't think I'll be allowed to go out and by an exfoiliater. So like a natural or homemade remedy? 2: What should I use on the bumps and the whitehead? Thank you.