I would assume you have been doing these hand springs for quite some time. Handsprings take a lot of practice to perfect. You likely have been wearing out these cervical joints. The head back position puts the spine into a straight line which takes all of the impact absorption out.

You may have given your brain a good shaking but it sounds like you surely gave your cervical (neck) spine a rough time. The joint between the skull and C-1 vertebra has no tolerance for impact. Jamming it together can cause the nerves to be traumatized. This can be dangerous.

80% of concussions have an upper neck injury component that causes concussion like symptoms. It sounds like you got the neck injury part of the trauma.

Vertical compression is pushing the two bones (skull and C-1, C-1 and C-2) together. This can bruise the surfaces. Whiplash is straining by using momentum to put joints at the limits of their range of motion.

You need to find a therapist, sports trainer, or such who can help you understand these issues and terms and the mechanics involved. They are rather simple concepts.

You should not be doing any more gymnastics until somebody has diagnosed what happened.

Did you learn handsprings on a gymnastic track that has give and then moved to a hard surface?