I applied for SSDI in January of 2016 and, although I have been disabled since a major surgery on 01/20/14, SSDI chose 01/20/15 as my effective disability start date. This decision means I cannot receive Medicare benefits until January 2017. This is not a correct decision by SSDI and I cannot find any info on how to appeal the decision. I am hoping you will be able to assist me.
Unfortunately, I don't think Social Security has made a mistake. You may well have met Social Security's definition of disability in January 2014, but Social Security will pay retroactive benefits going back only so far. In turn, Social Security will assign an "established onset date" going back only so far.
The rule is that Social Security will pay retroactive benefits going back only 12 months before the date you apply. Since you applied in January 2016, you can only receive benefits dating back to January 2015 (your "entitlement date"). You become eligible for Medicare 24 months after your entitlement date, which in your case means January 2017.
Just to clear up a little confusion, your disability onset date is not the same as the day you become entitled to disability payments. There is a five-month waiting period in between your established disability onset date and when you are entitled to be paid benefits, meaning Social Security will set your disability onset date to be five months before your entitlement date. What this means is that your disability onset date can be no earlier than 17 months before the date you apply for Social Security benefits. In your case, your effective disability onset date should be in August 2014.
I'm sorry that wasn't the answer you wanted to hear. You may be able to qualify for Medicaid until January 2017, if your medical expenses are very high, and your income and assets aren't.