Yes, I had a very similar thing, but when I first left home, and indeed I had to see the doctor who gave me some pills. They did not work very well but that was 40 years ago so things have come on since.

It passes and you learn to live with the natural and completely understandable anxieties of living your own life, away from the nest and being aware of your own mortality. Don't let it interfere with the freedom and energy of your one and only youth! Hope this helps.