It's normal to feel scared about starting new life endevours. It's normal to feel anxious about future life goals especially big ones concerning your entire career. You're in charge of your anxiety, don't forget that. Your anxiety does not have the power to hold you back, only you do. There are tons of people out there who are riddled with anxiety, shaking, but they still force themselves to do it. I know it's extremely hard because I also deal with anxiety.
Anxiety is a normal human emotion. It might feel like it has power over you, but it doesn't.

You don't have to deal with patients if you don't want to. You can still work in the health field in another specialized skilled job that doesn't work directly with patients. And you can also go into another field that helps people in other ways. Don't paint yourself into a corner and think, "I have to go into this field, otherwise I'm a failure" the sky is the limit and it takes a lot of job shopping before you find one that fits.
Be open to failure, because even the most intelligent people make silly mistakes now and then.