Hello. Sorry to hear you've been feeling so horrendous, OP.
I've had this (in bouts) for years, too. There have been times when I've been totally non-functioning because of it. Pacing around in the night vomiting from anxiety, etc. Not been able to concentrate (or even make it into) work sometimes (and my job is very dependent on concentration and clear thinking). I think (in retrospect) at times I've been terrified of letting the anxiety go because then I might take my eye off the ball and not spot something serious (in me or DC).
Also, like you OP and Notso, I try to combat without meds (with the exception of a few weeks on Citalopram 10 years ago). I had limited success with CBT techniques - I found it really fed into my tendencies to over-think. But recently I've started using mindfulness meditation (not woo - just learning to be present - and I think has a lot in common with what Monikar says) and (although it makes me nervous to write this...) I think it's really helping.
I've had a couple of "aha" moments in recent months, when I've felt the anxiety start to build in a way which would almost certainly have led to a big flare-up in the past, and then been able to watch it dissipate through using some of the mindfulness techniques. This is not to say that I won't have many more flare-ups in the future (I'm sure I will), but I feel a lot calmer about handling them.
I don't have much experience of going to the GP about the health anxiety, as opposed to with numerous physical health scares, but I have heard that some people's GPs can be brilliant about it, so it might well be worth a try.
Let us know how you get on 