Wow, I am so sorry this keeps happening to you. I can only imagine how very very frustrating it must be.
I am a teacher, too. I taught high school prior to my concussion but have been unable to be in the classroom since my concussion. Between the painful physical symptoms, the cognitive difficulties I was having being able to multitask and respond in a timely manner, and the emotional lability, the classroom was just a totally inappropriate environment for me after my concussion. I am hopeful that someday I will recover to the level that I will be able to teach again, but at this time it is just not possible.
I "pushed through" my symptoms for the first week after my concussion and ended up making things much worse for myself. So, just make sure in your eagerness to do your job and have people think well of you that you don't end up hurting yourself in a more permanent and damaging way. If you were a PE teacher and kept injuring your leg, you would not keep pushing yourself to run with the students just because the school was short-staffed. Just because your injury is not visible does not make it any less real or valid.
As for the recurrent head bumping, I'm wondering if you have had any vision therapy or a vision efficiency evaluation? After my concussion, my eyes had difficulty working together. I could imagine that something like this might make it difficult to tell exactly where you are in space. Vision therapy or possibly prism lenses might help.
You can find a doctor who does VEE testing at
http://www.braininjuries.org or
http://www.nora.cc
Good luck, and please do take care of yourself. You're important!!