Health anxiety - how to deal with it?

I found a very good answer to this question in the book "The Art of Disappearing" by Ven. Ajahn Brahm.

I quote the relevant section below from page 6 of the book.

It’s the same with the aches and pains in the body and with sickness. When you meditate, remind yourself they’re none of your business; they’re the body’s business — let the body look after them. Thinking like that is actually a powerful way of keeping the body healthy. It’s a strange thing that sometimes the more you worry about this body, the worse it gets. If you disengage from the body, sit still, and just allow the body to disappear, it tends to heal itself. It seems oftentimes when you try to control and organize things they only get worse, and it’s the same with your body. Sometimes, when you let it go and just relax, the body becomes so at ease that it heals itself. So just let go and forget about it.

I’ve known a lot of monks whose health problems disappeared through the power of their meditation. The first time I saw that was with Ajahn Tate. When I first went to Thailand in 1974, he was in the hospital with incurable cancer. They gave him the best possible treatment, but nothing would work, so they sent him back to his monastery to die. He died twenty-five years later. That’s one example of what happens when monks “go back to their monastery to die.” They go back and then live a long time. So you disengage from things — nibbidā arises — and the mind turns away. It’s had enough, it doesn’t even want to look at them anymore, and you find that they fade away.

This is the process you read about in the suttas, nibbidā leading to virāga, the fading away of things. When you regard something as none of your business, it fades away from your world. Consciousness doesn’t engage with it anymore; it doesn’t see, hear, feel, or know it. The way this works is as follows. Whatever you engage with is what takes hold in the mind — it’s where consciousness finds a footing and grows. you are building mental edifices. It’s very clear to me as a meditator that we create our own world. But when you disengage, you have no business there, and because you’re not interested in it, the whole thing just disappears from your consciousness. When you have nibbidā you’re really “un-creating” your world.

Anxiety is clinging to a predictive model of the world which does not accurately predict sensory experience (wrong view).

The Buddha's prescription for all anxiety is the same:
Summon the courage to release your biases (āsava) and strive to see the world the way it actually is. (yathabhutañanadassana)

How?
Seek out worthy teachers and test their hypotheses thusly:
Does this hypothesis correctly predict my sensory experience?
To the extent to which it does, trust them and inquire more deeply.

My favorite teachers in the area of health include Doctors Steven Gundry, Sten Ekberg, Eric Berg, Robert Lustig, Thomas Seyfried, Robert Malone, Pierre Kory.

Reassurance from doctors or knowledge doesn't really work. I know it experientially.

Doctor's reassurance results in finding another doubt where the former one has been patched. It is temporary ease in the cycle of aversion and desire, typical samsaric, vicious cycle. Aversion from feeling anxiety and feeling ill that results in the desire of reassurance is the main agent that spawns endless knots, knots that have even aversions towards knots. Mind is quite crafty and will always try to find a hole in the new logic-driven defence line. It is, therefore, not through intellectual reassurance that one gets released from such trapping. Wisdom should arise naturally, through a mood change, when body and mind are calm.

Now, for being trapped in anxiety best you might do is to focus on breathing and note that you are feeling anxiety, if you are feeling pain, then note that you are feeling pain, all with kindness if possible. Then, thoroughly check your body reaction(s). Try to do mindfulness of scanning the body down and notice these tensions. For instance, typically you will have tense abdomen muscles and tense jaw area, mindfulness of the body will let you see it as its a fight or flight response. Muscles should then let loose after acknowledged, furthermore, combined with breath - worry will wane.

Another thing is not to cling or have aversion to anything and importantly, remember three characteristics, especially impermanence - everything will eventually die or dissolve. We should not feel aversion toward chronic, or terminal condition, illness.

We have to navigate through confusion to calm abiding, illuminating clarity and make peace with the bodily condition.

When the patient feels sensation, he can practice Kayanupassana(mindfulness of the body) and Vedananupassana(mindfulness of feelings). When the thoughts of worry come to the mind the patient can practice Cittanupassana(mindfulness of mental activities) and Dhammanupassana(mindfulness of realities).

This technique will reduce the worry that leads to anxiety.