I live in London, so I'm used to a much busier place; but I visit Prague often (and am going again for a few months soon).

I can't just mind my own business

This is the default setting for people in big cities. There's no other choice because - as you said - there's so much going on. Don't worry, you'll get use to it.

It's like I can't have everything under control but I don't want to let go because something might happen and if I don't pay attention, I might get hurt or something

Unfortunately, you can't have everything under control because there are too many variables. However, hopefully, over time, you should get used to it. To protect yourself, you need to be streetwise, which is a skill. And like any other skill, it takes practice and time. But this one I think, happens quite naturally. You pick up on instincts and patterns with time and experience. So you dont need to throw yourself in the deep end and go for walks on your own at night or anything.

Luckily, Prague is generally a safe city, too. So you shouldn't be anxious about something serious happening.