I have anxiety issues, too. I don't worry so much about my health issues... just a zillion other things (I gotta laugh about it or I'd cry! - not trying to make light of anxiety).
I can only tell you how I cope. First, I *try* to avoid all anti-anxiety meds. They work and help some people. I can't take them because they impair my ability to function as a parent (I feel loopy, no memory, etc). I only take them at my absolute worst - and there have been a few times. (Side note...I only get "side effects" from there meds... not from narcotics or anything else. Weird.)
My biggest thing I've learned, though, is I've wasted so much time worrying about things that never come to fruition. My faith (I'm a Christian) - says we aren't to worry... and that worrying is actually a sin. (I know - no religious talk here... just a quick comment). But, as strong as my faith is - how do you turn your mind "off" when you have anxiety?
I use distraction. I keep busy. I laugh a lot and try to find humor in how crazy life is. I've had some BIG life issues that have caused lots of worry.... and, in most cases, the situations turned out FAR better than expected - so, again, I wasted so much time w/ my anxiety issues.....
And, even if the "worst" happens - you deal w/ it, right? There is really no other choice. I don't mean that as harsh as it sounds... and it's something I have to tell myself each day.
Oh, and the reason I don't worry about my health issues - in particular - is I really have learned that I have NO control over my issues. I can make my doctor appointments; take my meds; do the things within my control. But I do have several "progressive" components to my health issues - meaning, things ARE most likely going to get worse (I'm 38).
Now, I have moments of depression - everyone can tell you that here :) But, not so much "anxiety" and worry if that makes sense.
I'm rambling (as usual). Point is - I can relate. Do your best to try to calm your mind and "change" the "tapes" in your head.... and think about other things than what the "worst" possible outcome can be health-wise. I know it's not easy. Hang in there.