Hi Rachel & welcome. I'm not exactly an expert at social security so take what I say with a grain of salt. My understanding is that your son may qualify for SSDI but you wouldn't. You may, however, be his representative payee, which means his payments would be directed to you to cover his needs. You will be made to account for the money annually. Here's a link with some info:
http://www.ssa.gov/pubs/10026.html