Congratulations on your upcoming marriage! And you can rest assured that getting married will NOT affect your eligibility for Social Security Disability benefits or for Medicare. Your eligibility for Social Security Disability benefits is based entirely on your own physical or mental condition (your ability to work) and on you personally having worked long enough (and paid Social Security taxes), based on your age, to qualify for benefits. It has nothing to do with your marital status or your spouse's income or assets. The same is true for Medicare. If you are eligible for Medicare either because you are 65 years old or because you have been receiving Social Security Disability benefits for two years, getting married does not affect that eligibility.
One thing that's a little unclear from your question is whether you actually mean eligibility for Medicaid rather than Medicare. Because you used the words "getting approved," it sounds like you might mean Medicaid, which you have to apply for. Your income and assets do not affect Medicare eligibility, but they DO affect eligibility for Medicaid. You can be eligible for Medicaid only if your income and assets are both very low. If you get married, Medicaid is permitted to consider your "household" income, not just your personal income, and that would include your spouse's income. If your spouse's income puts you over the income limit for a couple, it could mean you'd lose your Medicaid coverage.