Is is normal to feel like this?

No, that is not a normal thing to fear. It sounds like you have a fear of intimacy or public places. I used to be afraid of intimacy as well and would feel physically ill when people hugged me or touched me. I'm a lot better now, but not 100% better. I made it this far from trying really hard and help from people I love. A good idea would be to talk to a legitimate and certified therapist.

Paranoia and social anxiety disorder, Notice that both of those situations involved you being around a group of people, even perhaps a group of unfamiliar strangers.

Cause:

This distrust issue is a form of psychological trauma that happens to people who were abused by strangers or repeatedly bullied in public places such as "school/malls/neighbourhood".


Solution:

Building self-confidence "such as through martial arts, gym, or talking to opposite sex more often" and making more real life friends can be the best natural solution to this.


Medical Treatments:
Psychologists usually give anti-anxiety medication and an on-going session therapy. mind you the medication has mental side effects that can cause memory loss, inability to focus, and therefore affect your work/job performance.



Sources:
Experience, and lots of obsessed study :D

Sometimes the world is overwhelming and certain places can be hard to deal with. Not everyone feels okay in a crowd, much less a crowded room. It may not be "normal" but it isn't wrong either. How many times has this happened to you? How often? If its every time you are in a crowded room or in a place with lots of loud noises, stay away from such places, find quieter places with less people to interact with the world around you. It's not about feeling like you can't go to these places, but if you want to be kind to yourself, accept your anxieties, talk about them with those that love you and support you, perhaps even seek out professional help if you can afford it, if you can't - research online what your triggers might be and how to avoid them. We all aren't perfect, I sure as hell avoid public places with crowds. It's all about knowing what affects you and how to handle it with new behaviors. Sometimes facing the fear head on is the only way to conquer it. (I go to busy places once a month like a mall, and just force myself to walk through the crowd to the other side of the building. It's helped me in small increments be less anxious.)Don't be afraid of the anxiety, learn to understand it, accept it and work with it to conquer it.

We all have different things that make us feel the way we do.We all have also been through different things to other people.
If I am right here,Id say that you have been through some things that are still bothering you and that quite a lot of us have also been though,so you are not alone in this.You might find it helpful to talk to some one though about any thing that been going on in your life that perhaps you haven't yet been able to open up about.
As to the question you ask...Is it normal,yes for you it is.Think about this for a moment.?
If you where asked how would you feel if you were left on a beach all by your self for 2 days?,I am sure the other students would have different answers to yours too.Just depends on whats been gong on with them in their life.
One student might say that they would feel calm and would be sleeping most of the time,because they find the sounds of the waves calming and haven't had much sleep in a while.While another for example might say..They would be terrified and would be trying to find a way to get off the beach .That may be because,when they were very small they almost drowned on a family holiday at the beach or something.
So we are definitely all different and we all have different life experiences.

First off, 'normal' is a very complicated term. How do you define normal? You can't really, since everyone is so different from each other. But you're already questioning the fact if your behaviour is normal or not, so you see something you're unhappy with... The way you react is not bad at all, ok? There has to be some kind of background as to why you react the way you do, but I don't quite know about that... Please don't put yourself down, though. Maybe just ask yourself WHY you react the way you do? Then think about how you want to act instead. Only if you wish to change. If not, that's perfectly fine, too.