My wife and I are filing separately but it appears TurboTax is showing us filing jointly. Where do I check this?

When you went through the My Info section you were asked if you were married in 2020.   The next question was "Do you want to file together with your spouse?"   If you said "Yes" to that you began a joint return.   If you want to file married filing separately you have to answer NO to that question, but you will still have to answer some information about your spouse.

If I am filing a separate return why do I have to list my spouse’s information on my return?

Even if you file separate returns (the worst way to file) you each have to list each other's SSN's and some other information on your own tax return.  The IRS can then cross check to make sure you are not "double dipping" for itemized deductions, dependents, etc.

If you are in a community property state, there is more information that will be needed.

Community property states:  AZ, CA, ID, LA, NV, NM, TX, WA, WI

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

Why do you want to file separate returns?  That is usually the worst way to file.

If you were legally married at the end of 2020 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 $24,800 (+$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