I mistakenly filed Married Filing Separate and should have filed Married Filing Joint. How do I correct this? Will this cause me any problems with IRS/ NY?

You can look over your finances and decide for yourselves which path to choose.   Your own return can be amended so that you can file a joint return, or your spouse can file her own separate return.   Only you can evaluate which way comes out better for you.  A joint return will require YOU to amend the return that you already filed.

It is not easy to compare MFJ to MFS using online TT but you can do it.  Since you only get one return for each account and user ID, you have to use 3 accounts and user ID’s—one for MFJ and two for each of the MFS returns.  Compare, choose, and file—and pay—accordingly.

It is much easier to do this comparison using the desktop version of TT installed from a CD or downloaded to your own computer.  You pay once for the software and you can prepare multiple returns easily, and it has a “what if” feature that allows comparisons.

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