It's interesting what you're describing, that you say you notice your mind is "searching" for something. This, I've been finding recently, is a feature of an anxious mind in general, whether inside the context of health anxiety or outside. Thankfully, I haven't had debilitating HA for many, many months, but I still do have an anxious personality, and I've noticed more and more that my mind almost "defaults" to obsessive thoughts, fixative thoughts, and worst case scenario thoughts. Just a couple of weeks ago, I literally SAW my mind move from one obsession to another as the first issue I was fixated on got resolved. I was like, "hey, wait a second, I saw that! What are you doing, brain?!"
All this to say that I think, as anxious individuals, our reasons for fixating on things—whether bodily sensations or otherwise—are deep and varied and take a very long time to work through. I admire your willingness to seek treatment for your anxiety—it can be a scary thing, especially because so often treatment acts like an onion; the more layers we peel back, the more issues we find we have that we didn't even realize were issues before.
For me, this has come about recently more through weight loss. As layers of literal protective covering come off, I'm learning all kinds of things about myself that I didn't know before—that my mind is quite comfortable defaulting to negative and miserable thinking is one of them. My nutritionist/therapist recommended a book to me called "When Misery is Company." Look it up if you're so inclined; G00gle has quite an extensive preview. I've never, in all my years of reading these kinds of self-help type of books, found myself so well-described in one of them. Scarily, it's me to a tee, and though the thought of challenging and retraining this kind of thinking is scary as hell, ultimately, I KNOW it's the key to (gradually) getting over all my other issues.
Working through HA is a process, remember that. Just keep swimming.