ANDY'S ANSWER: I'm guessing you weren't really being bullied for having pimples, but you were being teased. Somehow kids always know when you're going to be sensitive about something and they go right for making fun of whatever that is.
Also, annoyingly, I find the pimple medication ads perpetuate the idea that it's ok to make fun of someone who's had an outbreak of pimples. (For this reason I won't endorse their products.)
Although people can get pimples at any time in their life, when puberty hits and your hormones start kicking in, your glands may become overactive and produce more sebum than is needed. Sebum is a natural oil that your hair and skin needs. When there is too much sebum, your pores can get plugged and bacteria grows. That causes infection which causes swelling and redness which is a pimple.
Your best defense is to gently wash your face twice a day - Don't scrub your face. That can actually cause more irritation. Only wear makeup or sunscreen that is noncomedogenic - oil free. Try to keep hair products off of your face. If you have been sweating or are in an environment where you are exposed to dirt or grease, it is a good idea to wash as soon as you can.
Below is the recording of Andy answering this question.