Christie, your explanation does not appear to me to be DOMS. DOMS would be a tightness and slight ache a day or so after the workout. The more you workout the less and less it will happen and eventually your body will adjust to it. I am always searching for that feeling as it is far and few. The only time I get it is if I take a break and come back; or if I change things up majorly. It sounds like you pulled something and you are not allowing it to heal properly and you are re-aggravating it each time. I would R.I.C.E. it and stay off it for 4-6 weeks and then try again and see if it reoccurs; if so then seek medical attention.
As for your dizziness, to me it sounds like you are not getting enough oxygen. Have you ever been tested for asthma? What you may be experiencing is "exertion" asthma that only comes from doing high levels of activity and wouldn't affect you other times. When younger I was diagnosed with this and used to use inhalers when doing high levels of sports and exercises. I don't have too many problems now as an older adult but that is because I know my limits; though I do push them. I would experience this in TKD from time to time; hated it. This is just an observation as I'm not a doctor.
Good luck with your training.
"IF I COME ... I'M BRINGING THE PAIN WITH ME"