Possible concussion/closed head injury?

There is no way a gymnastics trampoline should be surrounded by exposed concrete. Also it is worrying that you threw back so badly without even knowing what you did wrong (you're not supposed to throw back at all, you jump up and lift your hips up in front of you, then tuck to accelerate rotation.) It calls into question whether you been properly trained to do back somersault in the first place.

You really need to see a doctor because I'm pretty sure a minor concussion would have gone by now and this could be something more serious like a bleed. If what you say about the trampolines being surrounded by exposed concrete is true, and/or you were not trained to perform back somersaults properly, using appropriate progressions (like flat back) and support, then you can sue the gym for the medical costs. They will have insurance which would pay out under these circumstances (and probably insist on re-risk assessment of all apparatus and/or further training for staff.)

No. Until you blacked out completely, or began throwing up >3 times in a row, you do not need to go to the ER. You most often gave yourself a mild concussions, however didn't hit hard enough to intent a fracture or head bleed. Headache and muscle anguish can linger for every week or more.