I'm constantly worried about what I'm thinking. I have to always make sure that I'm not thinking something bad (sexist, racist, etc). I'm scared that I'll think the wrong thing. When I was younger (as in, a small child) I tried not to think at all in case someone could read my mind. Is it normal?

Try and separate the person's action from a general sexist or racist thought and figure out what they personally did that bothered you. Start training your mind to state the individual's actions rather than 'slandering' a whole group. Eventually you should start seeing the problems that bother you and can start dealing with the root causes.
Also it takes a creative mind to think others are reading your thoughts...
If you could read people's thoughts you'd find out your thoughts aren't nearly as interesting.