I suffer from health anxiety also but I feel my case is mild and have managed to research some techniques over the Internet to help me. I don't know exactly what your fear is, is it a fear of everything to do with your health or just certain things.
I could type lots about myself and what I do to manage things. With myself, I have a fear of cancer. Mainly Breast Cancer. I have had a small family history of BC (which had a good outcome) & with all the publicity about it all the time it does make me rather anxious at times. I now manage my anxiety as best as I can with the things I have taught myself.
One thing I did come across in my research is this and I try to remind myself of it.
"if you accept uncertainty you worries will go away but if you don't accept uncertainty your worries will stay". We have to be at peace with what we don't no and some things are out of our control. I certainly know its hard but when you can put in place some management techniques your anxiety should ease.
I have accepted that I don't think I will ever be free of getting anxious over health things to me now its how I manage it is what's important to me. I would wind myself up trying to make the thoughts totally go away and they never would so for me it's management.
good luck with it let me know how you go.