Do you think the psychologist can help me?

I think you should indeed go to a psychologist or if you really, really don't want to do that go to someone you can trust, for example a teacher, he/ she will help you. Or you can do it another way; even if you think you're better off alone, it's always very helpful to have someone you can talk to. So maybe you can join a sport club or start playing an instrument, or start a blog online.
A few years ago I was a very shy girl who didn't like talking at all. I didn't like music, people, or internet and I wasn't good at school (my very typical real life sob story). The people in my classes always said me and my twin sister were the same person, that I didn't really have a personality on my own. I didn't believe them, I mean i am the only one who knows myself the best. So I just ignored them and had no friends. I nearly dropped out but eventually didn't because I knew I 'd be in another class the next year and want to try again (conclusion: change makes that you can retry, which can make life so much better; but don't axaggerate it, stay being yourself, just show your other side).
Then I got into another class with these very kind kids. Even when I was shy at first, they accepted me for how I was, which is why I'm so much more confident about myself nowadays.
So what I am actually trying to say, is what therapists and all these other people would say as well; go search for people like you. I have never fit in, in anything really, but I don't care since I have friends. And seriously; I am no good at making friends. But there are people on this small planet who don't care about that and accept you and befriend you and help you.
Okay so to make a very long story short, I think it'd be good to go to a psychologist but also try to find people (not forced then) with who you can talk. It makes life so much happier. ;) and you then have a reason to go to nice friends instead of listening to your parents. Maybe they only want you to have friends which is why they act like that.

So that was my advice, I hope I could help you :) My own story is not really relevant but maybe it will help you as well, so that you know there are so many people who want to help you. You just haven't met them yet (or you do but you don't know yet). A psychologist can be one of them.

And uh, as second thought, you could confront your parents with it, just to see how they react. Maybe they will help you; if not, remember it doesn't have to change your life.

Plus I think you are very strong, because some people really try to blend in and do all kind of things they actually don't want to do but they eventually break; but the only way to be happy is to be your unique self. Not everyone on earth is beautiful, but people (like you) who want the best for others and for themselves are.