I am the fiduciary for a trust and need to generate a K-1 for myself. How do I do this? Which Turbo Tax do I need?

You will need the TurboTax Business Edition to file the Form 1041 Trust tax return and to generate a Schedule K-1

TurboTax Business Edition - https://turbotax.intuit.com/small-business-taxes/

The Business Edition can only be installed on a Windows based personal computer, not online or on a Mac.  The Business Edition cannot be used to complete a personal tax return, Form 1040.

I had my accountant (at the time) file a trust tax return (a few years ago), and the estate didn't have any income in 2022. Is there a way to generate a K-1 without having to file a tax return?

No, Schedule K-1 is part of the 1041 trust return and can't be created by itself. If the trust is not required to file a return, the Schedule K-1 is not required either. 

But I received taxable income from the trust that needs to be declared on my taxes. Thoughts on my next steps?

The trust would have to report the income on a trust tax return. You would then get a schedule K-1  from the trust tax return to report the income on your personal tax return.