Neurological is another disability classification that you could look into.
Do the states differ on what the actual categories are? Because I don't think that exists here. They have Traumatic Brain Injury and Cognitively Impaired (I think it's called), which would be kids with low IQ. But no "Neurological".
Yes. Sorry, I was thinking of the states I'm familiar with. If neurological is an option in your state, it has the advantage that the impairment doesn't have to result from a TBI; it can be from any origin, as long as there is a neurologist's dx. Cognitively Impaired is usually in its own category (previously Mental Retardation in the federal law, recently changed to Intellectual Disability).
Some states are actually non-categorical, and have eligibility guidelines based on needs and services, without disability labels.