If you were incarcerated or not should be part of public records.
By writing the DOC emails and letters formally asking for those records you should be able to attain them. Another alternative to get the records from the DOC is to file to receive those records under the Freedom of Information Act.
I am not familiar with Social Security regulations in this area. However, I am aware that many governmental agencies can withhold cash benefits, tax refunds etc. to recover costs from things like incarceration, fines, judgments, child support etc.