Before I start, I would like to remind people that I do not work for the social security administration or social and rehabilitative services. I have been on SSDI since Aug. 2001, and between then and now I have become familiar with applying for benefits by working with other CVSers and their families.
SSDI verses SSI
The first thing you need to do is determine which form of assistance you, or your child, may qualify for. Both SSDI and SSI are administrated by the Social Security Administration.
SSDI - social security disability income
In order to qualify for SSDI you must first meet the definition of disability established by social security. You must also have recent substantial employment. SSDI is based on how much you have already paid to the system. (that's what the FICA on your pay stub represents)
SSI - supplemental security income
In order to qualify for SSI you must first meet the definition of disability established by social security. SSI is awarded to disabled individuals who do not have a work history. Children, housewives, etc.. SSI is designed to help low income families, so the income of all the people in the household are considered before benefits are awarded.
Both SSDI and SSI can both be awarded; however, you will recieve the larger amount. You can't "doubble dip".
The best website to reference disability is http://www.ssa.gov/disability