While there are a lot of ways around getting rid of the "erms" and "ahhs", getting over the awkward/nervousness of it all is a bit different. Course you can simply edit out the awkward parts, but you can't really edit them out of your life, right? So with that in mind, let's move on to something better!
A few good methods would be to keep some cue cards ready so you don't lose focus of what you're talking about; they don't have to be full on scripts mind you, just something to keep you on track. Another trick would be to talk to the camera for awhile, recording or not. Just prop it up, hold it, whatever you are going to do and have a conversation with it. Now, I know this seems silly, but that's the point. Once you are doing something so ridiculous by the time you are actually recording, it won't seem as awkward. Plus, I feel that gives you some time to relax, and get prepared for the real thing!
As a person whom suffers from both depression and anxiety heavily, I completely understand where you are coming from, and it's not something you can just "get over". I know with work, and some time you'll be able to conquer this. If you need any advice, or help on anything please don't be afraid to ask!