You can get a concussion without your head hitting really hard. If it were me, I would get assessed. Obviously, the treatment is rest and no electronics, heavy brain work, but I would want to know. When I hit my head a couple of years ago, with the car door, I am *sure* I had a concussion. I didn't go to the ER and it was probably a dumb idea.
I have low blood pressure most of the time, so I get the dizziness thing you are speaking of. My DH has it too, along with his motion issues, so he has to be extremely careful in tabata class, with all of the getting up and down.
Rest up!