Hi and welcome to NMP, Victoria
As an OCD sufferer I can tell you straight away that there is a known theme in OCD commonly referred to as Schiz OCD which covers this. You may come across it as a theme of the "Pure O" end of OCD. In reality, medical literature don't consider these terms and look at the real obsessive-compulsive behaviour so these "themes" are often explained by the charities as they are non medical terms that sufferers use to talk about their OCD.
There are quite a few threads about this, some on this board, some on the GAD board and some on the OCD board. I will have a look and post you some to be going on with but I'm sure one or two active members will also spot your thread and comment on their experiences of this.
Like all forms of anxiety, the Cognitive Distortions in play will cause your thinking to be negative and skewed. This means you will focus on things that fit to your worry and not look for things which disprove it (Confirmation Bias).
You give a good example of one of the Cognitive Distortions - all-or-nothing thinking (dichotomous reasoning). We want an absolute, a yes or no, a 100% answer or we feel we can never truly accept. But this is false because life is full of shades of grey, as is medicine when they are working through processes of elimination to find the most likely remaining possibility. We have trouble accepting this because the fight or flight response is basically built to find something definitive and why e.g. that bear is charging at me and my spear is broke so I'm running away because it will kill me.
Schizophrenia is the most common mental health illness concern but you see others too e.g. bipolar, delusional issues, etc. Really it can cover any including such as the organic ones like dementia. The basic issues are the same.
There are differences in how our doctors diagnose what falls under HA between the US & UK. This is because we use the WHO manual, your doctors use the US derived manual. This can mean differences between what disorder they diagnose but it's still essentially an anxiety disorder, sometimes it's just a different name. GAD, OCD or "Illness Anxiety Disorder" are the ones in the US manual. The latter is actually an OCD spectrum disorder (we don't have a spectrum in our manual) so it could fall under either BUT essentially yes this is well covered under anxiety as a whole.
There is an excellent website by a guy in the US called Steve Seay and I think he has articles about this. He's a licenced clinical psychologist over there and I found his articles extremely helpful in understanding finer details that the charities in the UK leave out. They would be worth a read to you.
I will dig you out a few threads I know of so you can see what others have said.
---------- Post added at 05:03 ---------- Previous post was at 04:58 ----------
Here are some threads. The one created by ChocoOrange has a post in from me with links to several threads about schizophrenia worries in OCD:
http://www.nomorepanic.co.uk/showthread.php?t=177028
http://www.nomorepanic.co.uk/showthread.php?t=177300
http://www.nomorepanic.co.uk/showthread.php?t=174792