I wonder: do you even have to reveal that you left without two weeks notice? I assume you're not relying on this recent employer for a reference?

I agree with the 90-day probationary period reasoning. It wasn't a good fit for you, and you would rather put your skills to work in an organization that is far more suitable for your skills and professional working style. That's totally reasonable to say and explain to prospective employers.

I worry that by professing anything about your emotional state (about not giving two weeks notice) that it may make other employers uncomfortable to hire you.

If you're not relying on them for a reference, then it shouldn't really be a problem. Contact other references and let them know you're looking and ask if they can give you a positive reference. Then just rely on those references. And be confident! HUGS.

ps. I quit TWO jobs on the spot and landed on my feet both times.