Teo
I know exactly the sensation you are talking about. I still have this sensation, though it has diminished quite a bit over time. Some will try to tell you it is anxiety, but I know that it is not. Your anxiety can be very real, and this physical feeling of your brain moving around in your head can be very real too. But it is not a phantom feeling that is "caused" by anxiety; at least not for me.

I don't know what causes this physical sensation, but I believe it is some combination of a neck injury, changes in blood flow to the brain, vestibular damage, and an oversensitive PCS brain that notices everything a lot more.

What helped me was a good neck PT that helped heal the soft tissues in my neck, A great vestibular therapy team, time, patience, more patience, light to moderate exercise that didn't aggregate my neck, good sleep, etc... You also have to try not to obsess about these sensations (I know, easier said than done). Try to focus on what you can do without aggravating symptoms, and focus on trying to find good PT providers. Get help from your family.

I can't go for 5 mile runs of play hours of basketball like I used to, but I can fast walk, play a bit of basketball, and go for some light bike rides. I have to accept that as enough and carry on with my life.

Hope this helps.