If you are legally married then you should be filing as either Married Filing Jointly or Married Filing Separately. If you have a qualifying child as a dependent and you have not lived with your spouse at any time during the last six months of the tax year then you could file as Head of Household.
You will need to file amended returns for each tax year you filed as Single when you should have been filing as Married. If you do not have a child as a dependent then you would file as Married Filing Separately if your spouse does not have a Social Security number or an ITIN. You would write in NRA in the box for a spouse's Social Security number on the Form 1040.
See this TurboTax support FAQ for amending a tax return originally completed using TurboTax - https://ttlc.intuit.com/questions/1894381-how-to-amend-change-or-correct-a-return-you-already-filed
See this IRS website for further information on filing a return when the spouse is a non-resident alien - https://www.irs.gov/individuals/international-taxpayers/nonresident-spouse-treated-as-a-resident
