Those granted SSDI have to wait 2 yrs to get their Medicare. They usually qualify for medicaid during that waiting period. That makes me think you have SSDI - you were granted it 2010 and the medicare was suppose to be active in 2012.

Is your benefit greater than $750 a month? Because that is what folks on SSI get

Call Social Security not Medicare to get this straightened out. Also you can get a copy of your award letter on their (SSA) website and it should state what program you are in SSI/SSDI.