That surely is what 'normal' people do. I know because I've been one of those normal people up until recently until the HA started. Before my health anxiety I remember drinking ounces of coffee each day. I found the shaking of the hands and the rapid heart rate to be funny and jokingly talked about it with colleagues. I was going into extremely stressful situations (job interviews, certain dates, etc.) wired on caffeine and very nervous, but I didn't pay much attention to the nervousness and as a result it did not turn into anxiety. I also remember hitchhiking about 300 miles after having drank half a quart of vodka the previous day. After having a big cup of coffee on an empty stomach too.. Nowadays I can't stand in line at the grocery store after drinking the previous day or drinking coffee before...I also remember being really sick (flu or whatnot) and not paying much attention to it. Nowadays a single pain at any part of my body can trigger anxiety attacks..
So yeah..normal people don't pay attention to those things. It really is the normal thing to do, as you can't control what is happening to your body by thinking about it.
However, thinking about your anxiety is actually thinking about thinking itself, which is trying to solve the problem at the level at which it was created. Go into a situation that requires your full attention and completely gets you out of your current state and BOOM.. you are no longer thinking about whether or not that itch you have is a result of liver cirrhosis.. The thing is if you think about how you are going to feel in that situation beforehand you don't see the benefit in it as you are in your current state right now..
Ultimately, I still haven't found a solution. But thinking about it will not do anything. Doing something will.
Also, no you can't trust your body(it's not actually your body, but your thinking mind that interprets harmless things as big). I have lost count of the number of times I was honestly completely sure I was having a heart attack or was going to die. In reality I am very fit, have no health problems and anxiety is the only thing. It really is ruining my life.