SSDI comes with Medicare, SSI with Medicaid. However, if one is on SSDI, it takes 2 years to become eligible for Medicare (and one may be eligible for Medicaid in the interim) and if one is receiving both SSDI and SSI, whether one receives Medicare or Medicaid is more complicated.

I would talk with your Social Security office to understand if there will be any change in your insurance status should you marry. SSDI and Medicare should not be as changeable since it is based on your Social Security benefits that have been paid for and are individually yours versus just disability needs based on income from you and a spouse together.