If I failed a psych evaluation because a doctor said I was too nervous, can I get a waiver?

As a psych evaluation is not a normally required entrance test done, there is more to the story. And I don't think sharing your medical situations is a great idea on an open forum.
Are waivers approved, well yes for many things..
But the possibilities of yes or no are endless and without detailed information and a knowledgeable recruiter current on all the business rules in place this minute, plus review from an MD familiar with current standards of medical fitness for entrance into the service you are going to get guesses at best educated guesses, but still guesses.
See your recruiter, ask what specifically the issue is you are being denied for, then seek expert medical opinion on that.. If the new MD disagrees with previous diagnosis , than back to the recruiter armed with that info and say..WHAT NOW?

There is more to this story. You may not know, or you do.

What was the specific diagnosis, as there is no diagnosis for being nervous.

Do you have a personality disorder? if so then no
Anxiety disorder? If so then no.
do you take meds? Depends on the meds
do you crap yourself at every traffic intersection ? Then no.
find out the specifics.

MSG Bo

That is among the most retarded psych evaluators I've ever heard of. And I've seen a psychologist that'll give just about whatever recommendation a captain asks for in regards to a soldier. Screw them they don't know what their talking about.
I would talk to your recruiter if I were you, and if he's a jerk and won't help just go to another recruiting station. Don't let some bureaucrat's ego get in the way of your service.