Applying for SSDI will not impact anything. The injuries themselves are the issue and there is nothing you can do about that at this point. And yes, I doubt you can get coverage on brain injuries in the future unless you find work for a government agency that self insures and doesn't have a clause about pre existing conditions.

If your doctors are expecting you to improve you're going to have a very difficult time getting approved for SSDI, unless you qualify for a Listed Impairment. The earlier you file the more backpay you'll potentially be entitled to though, so it's up to you.

If you can hold out for a bit so your doc can determine if there will be lasting complications that will prevent you from working, then you can apply later on and receive benefits going back 12 months. For example, if you received your last concussion on 6/2013 and apply for SSDI on 1/2016 with an Alleged Onset Date of 6/2013, you could receive backpay from 1/2015.