Anxiety-related dizziness unfortunately is not something every doctor/ therapist knows about. It is under the class of vestibular disorders of which a subset is most certainly caused by consistent anxiety and panic. You will notice when you get dizzy, tension manifests in the back of the neck/ scalp region. I see some researchers looking for evidence that vestibular disorders cause anxiety. In every case I've seen, this is most certainly false- the anxiety came well before the dizziness, although I'm sure there are exceptions.
This kind of "dizziness" can be hard to describe, some describe it as vertigo, some as unbalanced, some as depersonalization, and on and on.
For this stage of anxiety, the main advice I've heard for recovery is basically to try to walk as if you didn't have it, and walk as much as possible, and don't try to make it stop. If you do these things, you will agitate yourself and it may get worse at first, but if you stay consistent, and build momentum, it gets better. It's important to make it a point to walk a lot, or you never build confidence that says "I can do these while feeling hazy and unbalanced." If you can build enough momentum where you feel like it really doesn't matter whether the symptoms are there, because you are going to do what you want to do regardless, that's when they usually will finally start to subside. I know that seems far off, but small steps.
Some doctors and therapists will tell you it's related to your breathing habits when you have panic, but that's an entirely different thing. This is an ongoing vestibular disorder due to a mix of tension and possibly atrophy of the part of the brain which processes spatial recognition (these are the best theories out there right now it seems, if anybody knew more I'd love to hear). And yes atrophy sounds scary but it's not, there have been plenty of people who fully recovered from this.
On a last note, sleep is important here, do whatever it takes to get on a consistent schedule that makes you feel somewhat rested.