I filed my tax return directly with the IRS in Dallas. How can I submit an amended return as well as file my state taxes for living in NJ and working in NY.

You will not be able to use TurboTax to prepare a "stand alone" state tax return.  When you use TT, the information flows from the federal return to the state return.   So....you are on your own to prepare a state return.  

 

Try going to the state tax site(s) to see if you can prepare the return there, or seek local paid tax help.

 

 

https://ttlc.intuit.com/turbotax-support/en-us/help-article/state-taxes/contact-state-department-revenue/L9qVToi02_US_en_US?uid=m6e06um0

 

 

 

 

 

As for amending the federal return you prepared somewhere else:

 

 

CAN I USE TURBOTAX TO AMEND IF THE RETURN WAS PREPARED SOMEWHERE ELSE?

 

If you did not use TurboTax to prepare your tax return, it is possible to amend the return using TurboTax but it will really be a pain.  It would be better to use the software or service used to file originally.  If a paid preparer made a mistake on your tax return, that tax preparer should do the amended return for you at no charge.

In order to use TurboTax to amend your return, you need to purchase the desktop software for the tax year and re-create the return EXACTLY as it appeared when it was filed with the IRS/states.  Every line has to be the same.  Then you have to "trick" the software into thinking you filed by saying you will mail the return. (but do not mail it)   AFTER that, you use the software to prepare a Form 1040X, which has to be printed, signed and mailed to the IRS.  It takes the IRS about 4-6  months to process an amended return

 

You have income from one state and live in another state.   So you will have two state returns to prepare.   They will have to be filed by mail.

https://ttlc.intuit.com/community/state-taxes/discussion/multi-state-taxing-moves-other-state-tax-dues/00/3397200