If you are legally married as of December 31, 2020, then you must file as either married filing jointly, or married filing separately. Joint filing is allowed even if you did not live together, but you must agree with your spouse to do this and you must agree how to divide any tax responsibilities or refund. Sometimes this is impractical during a divorce or separation. Usually, someone in your situation will end up filing as married filing separately.
to qualify to file as head of household, you must have lived apart from your spouse, and paid more than half of the expenses of keeping up your home where you lived, and provided care in that home for a qualifying person, usually a child dependent. The TurboTax interview will guide you on whether or not you can claim a person as a dependent and qualify for head of household or you could post more details about your situation here. Without a qualifying dependent and without cooperation from your spouse, you must file as married filing separately.
