You have a few questions to address, but prior to addressing them, let me just say this: anything in your wallet, or your car, or any other material possession is not worth suffering great bodily harm or even death for you or a loved one. If one were to fear for one's safety despite complying with an armed assailant's demands, then action would be appropriate. In other words, don't get yourself killed over a couple of bucks and your driver license.
That said, find a reputable school that trains for life-like situations so that any confidence it instills is not false. That is, the scenarios played out for self-defense purposes have real-world application in addition or instead of any other sorts of routines.
Any method would absolutely help with depression and anxiety as it tends to take all of one's focus to perform. Conversely, if it is a poor school or training situation, it can add to it, but you can figure that out really quickly if you attend a few classes prior to signing up.
As far as being nervous, anything new can be nerve-racking, but with time, that subsides. Imagine how you felt in high school taking driver's ed compared to how naturally you might take to driving now.
Do you already have a school/teacher in mind?