I'm 25 and have never had a drivers license. My agoraphobia has never let me take the test. I have driven hundreds of times though illegally but I don't do that anymore. I plan on actually taking the test myself sometime in the coming months.
Don't worry about being late! believe me! You can do it!
I'm also afraid of accidents but more afraid of getting pulled over.
The more you drive the easier it gets. usually anyway.