I know exactly how you feel Beached. I've dealt with health anxiety for quite a while and also thought it might have been tied to my alcoholism. I also saw a lot of doctors and had a lot of tests done but would still fear something being wrong. Every little twinge in my body used to make me start googling to find out what it might be. If I saw someone else who was sick or heard about someone else who was diagnosed with cancer or something else I would start diagnosing myself, etc.
The solution for me has been a combination of therapy, mindfulness and meditation practice and spending a lot of time here. I also try to make sure i'm getting enough sleep and eating right.
The real crux of the problem for me though was accepting my anxiety for what it is, very similar to the way i accepted my addiction. I now know that for whatever reason, I am simply an anxious person. Therapy has helped a lot, but initially I went seeking a cure - so it would all just go away. There is no magic bullet that can just erase it though, so accepting it for what it is was half the battle. And to be honest I'm still working on that part but my daily anxiety has decreased significantly. I've also nearly completely eliminated my "googling" and other bad health checking habits ( pulse checking, blood sugar testing, etc...).
I've also accepted that it doesn't really matter what caused my anxiety - my drinking or maybe it was even before that. But at the end of the day it doesn't really matter..it's a problem that exists so I need to deal with it.