Here's a simple way of doing it.
The good part is that you already seem to know your problem: you have physical symptoms which you believe are caused by more than anxiety.
Take that problem and develop the alternative: you are actually quite healthy, and your symptoms are only due to the false belief that they are caused by some type of sickness.
Now, you have two alternatives. Analyze ALL the available evidence for each case. Do this over and over again. Eventually, there will be such overwhelming evidence against your false belief that you will start to believe the more rational thought. It won't happen immediately, but every time you have an anxious thought, just continue to remind yourself of all the evidence against that belief. Just because we believe something doesn't mean it's true...a lot of kids believe in the Tooth Fairy...
To analogize it, it's like watching the end of a football game, when your team is up by three touchdowns and 0:01 left on the clock, yet you somehow remain convinced there's a chance they could lose. If you take a close look at all that evidence, and do some analysis of the likelihood of your team losing the game, you will eventually see that it's essentially impossible.