It is normal to feel some doubt, yes, but that shouldn't cripple you. So if you feel those things, my question is whether there's any actual merit to them. What's the connection between feeling you're awful and your writing? Is it bad grammar? Bad plot ideas? Bad characterization? Bad dialogue? Bad spelling? Do you even know?
Literally all of those and more can be corrected at any time, especially if you're writing on a computer and have Internet access with which you can do research and find writing tips, so there's no reason to be upset by them—that's what drafts are for. If you DON'T know why you feel so awful, you're wasting your energy and should just get back to writing; the only way to stop being awful at anything, be it writing, art, music, sports, driving a car, flying a plane, or anything else, is to just keep doing it and learn from your mistakes. Any decent writer will tell you that they make mistakes, but they move forward and go back later. That, too, is normal.
You can also have someone else read your work and give you a more objective opinion, but if you're terrified of yourself that may not be possible or even the best idea at this point.
Also, consider that if you were ever criticized severely about anything else—even if it was unrelated to writing—that may be bleeding over. Keep things in perspective. The criticism of the other thing may or may not have been legitimate, but it wasn't about your writing. Don't hate on yourself.
And if you HAVE been criticized about your writing, you have two options: keep writing and get better, or give up and prove your critic right. But your success or failure is YOUR choice.