Just my opinion, but if you still have constant dizziness, I don't think you're ready to go back to exercising. If you do exercise, start very lightly (is the advice my PT gave me).
I noticed that walking would shoot my HR up, so I started checking my fitbit while I walked. If it shot up, I stopped and waited for it to come down, then I continued on. It usually didn't shoot up again on the same walk. I still can't walk very far - only about 1/4 mile.
The only exercise I'm able to do right now is to gently ride a stationary bike in my family room (I have been an avid cyclist for many years, so I am used to the pedaling motion and the bike is optimized to fit me well). Everything else is too hard for my brain to handle all the balance, etc., required.
I am only one month into this, but I thought it should have been a mild concussion with a quick recovery because I didn't lose consciousness or forget anything.
Jenn