Whether or not it's "normal" should not be a concern for you. Everybody is unusual and different from others in one way or another - so there's no point in worrying about being "normal". Nobody is, entirely.
The only reason to be at all concerned about feeling nervous in public is if the experience DISTRESSES you. Being a bit nervous from time to time is an experience that almost everyone has, and deals with...it doesn't get to the level of causing them any distress. If you often feel distressed, then it would be reasonable to try to do something about that.
On your own, you could make a point of being in public more often, rather like an explorer going into the jungle. You could start this by repeating trips to market, perhaps every day instead of once a week. And take your time. In this way, you are visiting the SAME public place over and over, and repeated exposure might lead to familiarity, and your nervousness might wane. You can then move on to some other public place, and repeat the process. If that's not practical, at least being out in public once or twice a day, every day, could go a long way to ending your nervousness.
If you prefer, you could easily find a counselor to discuss this with. A severe case of what you're experiencing would be called "agoraphobia", which is a very well known condition with millions of fellow-sufferers. A counselor could be very helpful, if this distresses you.
Best of luck.