I'm a native New Yorker, and I have been taking public transportation for my entire life. Even I was a bit nervous the first time I had to navigate public transportation on my own in a new country!
And, I have used public transportation in MANY other locations in my travels! But, normally, when I travelled, the first time I would use the local public transportation, I was usually with someone... a friend, a native, a boyfriend... not on my own!
When I began taking the tube on my own in London, I was totally afraid I would get lost, and be very late to wherever I had to go, and I was afraid I would end up in a really bad hood.
So, it is normal to be a bit nervous the first time public transportation in used on ones own, for anyone, no matter how experienced - but it WILL pass.
Don't sit next to strange men in raincoats.
Oh, wait, it rains here all of the time, so that might be unavoidable... scratch that.