I would definitely see someone about this. Whiplash can make you dizzy, it is possible.
The reason you don't want to take any advice online is because there are very important structures through the neck, including the vertebral artery, and various nerves, as well as discs that can be influencing your symptoms. It would be prudent to clear these structures with a qualified therapist as the source of the symptoms.
In the meantime, write down as best per your recall exactly what happened, how you fell, and what movements activities cause the problems you are noticing.
If no one has picked this up before, please explain your concerns. There are specific tests that can be done to confirm whether these symptoms are a result of other issues
Regards