Should I file married considering we both have filed single for the past few years but we are still married?

What?  You have been filing as "Single" when you are legally married?  Big mistake.  Or do you mean you filed as married filing separately---which is fine.  

If you were legally married at the end of 2019 your filing choices are married filing jointly or married filing separately.

Married Filing Jointly is usually better, even if one spouse had little or no income. When you file a joint return, you and your spouse will get the married filing jointly standard deduction of $24,400 (+$1300 for each spouse 65 or older)  You are eligible for more credits including education credits, earned income credit, child and dependent care credit, and a larger income limit to receive the child tax credit.

If you choose to file married filing separately, both spouses have to file the same way—either you both itemize or you both use standard deduction. Your tax rate will be higher than on a joint return. Some of the special rules for filing separately include: you cannot get earned income credit, education credits, adoption credits, or deductions for student loan interest. A higher percent of your Social Security benefits may be taxable. Your limit for SALT (state and local taxes and sales tax) will be only $5000 per spouse. In many cases you will not be able to take the child and dependent care credit. The amount you can contribute to a retirement account will be affected. If you live in a community property state, you will be required to provide additional information regarding your spouse’s income. ( Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI)

If  you are using online TurboTax to prepare your returns, you will need to prepare two separate returns and pay twice.

https://ttlc.intuit.com/questions/1894449-married-filing-jointly-vs-married-filing-separately

https://ttlc.intuit.com/questions/1901162-married-filing-separately-in-community-property-states

https://ttlc.intuit.com/questions/1894449-is-it-better-for-a-married-couple-to-file-jointly-or-separately

If married you cannot file "single" unless you have a court decree of legal separation with separate maintenance (very few states have that).  You choice is Married Jointly, Married Separately, or possibly Head of Household if you have a child dependent that lives with you and have been separated from spouse the last half of the tax year.

For past years filed improperly I suggest that you find a tax professional (not a store-front tax mill) but a professional that deals with the IRS.   There could be back tax involved but a professional might be able to mitigate that.