Why do my motor skills suck when I'm feeling self-concious and what can I do about it?

I’m pretty terrible at most things that require hand-eye coordination or motor skills in general, but I have observed that my suckage increases greatly when I feel self-conscious or like I am being watched. For instance, I thought I was getting to be pretty good at driving, but when I went to take my road test, I drove ATROCIOUSLY in front of the instructor. This is something I really would like to change about myself because a.) I would eventually like to get a driver’s license and b.) I imagine, as a future physics major, I’ll have to do labs and such in which I will rarely have privacy, and I won’t be able to afford being clumsy and awkward. How the heck can I fix my anxiety-induced klutziness?