I like your optimism! Amending a tax return is not necessarily complicated, but it is foreign to most taxpayers. But yes, you would simply select the option to amend your return, and update any necessary information on your federal. When you get to NY, TurboTax will ask questions about your NY income. Then you can go revisit your CA return as you should be entitled to a tax credit on your CA return for the tax paid on income earned in NY. See the TurboTax article below for more information.
https://turbotax.intuit.com/tax-tips/state-taxes/multiple-states-figuring-whats-owed-when-you-live-a...
