There are several possible causes for your mood swings and twitches. I would recomend, seeing a doctor. Mood changes can be caused by hormones in the body that can sometimes be regulated safely by dietary changes or, under certain circumstances, medication. In the mean time, there are exercises you can do to control your mood to an extent (not completely). Identify your triggers, what causes your mood to change. Next, imagine yourself in scenarios that would trigger a reaction and think about how you would like to react. If you practice this regularly on your own, eventually it will be more natural to have the reaction you practice. Also, a lot of bullying comes down to your responses, so as you control your mood better, either on your own or with the help of a doctor, try to project a confident, happy persona. Don't be afraid to laugh at yourself. No one's perfect, so it's ok you're not either. If you take things too seriously, you become a target for bullies. Be confident being you.

Like RR said, ask your parents to see a doctor, maybe a therapist. Just ignore what people say, they're no more powerful than you are.