Yes, there is an exception to the usual Medicaid transfer restrictions for gifts to disabled children of the Medicaid applicant. Your mother can freely transfer assets to you at any age.
The fact that you are receiving Social Security Disability Income (SSDI) or Supplemental Security Income (SSI) is sufficient proof of your disability. Fortunately, this means that we don’t have to get to your second question about whether your mother now could make good on your prior compensation agreement.
Because you didn’t cash the checks your mother gave you, that might be treated as a gift from you to your mother – in other words by giving you the checks, she already fulfilled her obligation under the agreement. In short, that would be a gray area that could depend on the mood of the person evaluating your mother’s application for benefits.
To read more about the Medicaid transfer rules, check out this article.