Now you made me look it up:

Verb

jury (third-person singular simple present juries, present participle jurying, simple past and past participle juried)

1. To judge by means of a jury.

wiktionary

So I guess both “jury” and “judge” would work in that context, especially in the context of “Don’t judge me”.

Not that it matters but why not use this opportunity to deepen my knowledge of my second language