“is it possible that different people react differently?”
Absolutely. You are the sum of your genetics, your environment and your experiences. No two people have exactly the same “equation” making up their personality. Everyone has traumatic experiences, but everyone deals with these experiences differently. Also, the effect of a particular experience and be completely different from the effect of a different traumatic experience.
“And that if two people underwent the same problem that one would possibly come out with a mental disorder and the other one be almost unaffected?”
Again, absolutely. That is why some soldiers end up with PTSD and some don’t.
“what would make a child not mention to their parents that they were being sexually abused?”
Even if a child felt that what happened was wrong somehow, if an adult tells them it is a secret and they mustn’t tell anyone they often comply. After all, small children hate getting shots but comply because adults tell them they must.
Also, at age three you might not have known how to describe what happened to you. In addition, if this was a family member or friend of the family that most family members liked and trusted, a child would have a very hard time trying to convince anyone including themselves that this “good person” is a bad one. Children get very used to being told that they are wrong and adults are right.
As others suggest, you need to see if you can talk to someone about your past and the effect it is having on you. Ideally, your mother needs to do the same. Your mother may be seeing you as an extension of herself, or she may be trying to ignore your information that someone was evil enough to do this to you when she was supposed to be protecting you. She may feel a lot of guil;t if she lets herself believe you.
Good luck. You can get past this if you want, and so can she, but it will take hard work.