¡Hola TomW38 y Steven-W15!
In our Spanish team's experience, no me pongas nervioso/nerviosa "don't make me nervous" is used much the same in Spanish as it is in English; we're not familiar with it being used as a kind of colloquial expression. However, we have been able to put together a list of expressions that could be used when another person is being overbearing or threatening as you describe, TomW38. Perhaps one of these is the one you're trying to remember?
1) No me rayes - this means No me molestes, déjame en paz "Don't bother me, leave me alone."
2) No me calientes la cabeza - this is essentially Déjame en paz "Leave me alone" or No me provoques "Don't provoke me / Don't push me."
Latin American Expressions
1) No te me pongas al brinco - this is like No me provoques and can be thought of as "Don't try to threaten me / feel you're above me."
2) No me estés chingando - this means "Stop nagging at me / making me upset." (Be careful using the verb chingar in other contexts, as it can have very vulgar meanings!)
3) Si me buscas, me vas a encontrar / Si me buscas, me encuentras - This is like saying "If you want trouble with me, you'll get it."
I hope that those are helpful!
And indeed, a woman would say No me pongas nerviosa (with tú) or No me ponga nerviosa (with usted) to someone else.