Does English slang have a feminine version of "breaking someone's balls"?

Yes. Now stop getting on my tits. From Urban Dictionary,

To be really annoyed by someone or something and to express it in a funny exclamation

In lieu of a sufficient gender-correct alternative, I've actually heard women use "busting my balls" for themselves, though one's gotta be a pretty tough chick to pull that off.

Busting [someone's] chops is entirely neutral as is getting your goat, and depending on the scenario you might say he's on my ass about this or that...

Busting someone's balls generally, where I live, is more about getting on to someone about something - sometimes just to get a rise out of them, often to take them to task over an issue. Busting chops is generally more to get a rise as is getting someone's goat. So more commonly here, like if you have a harsh boss that is demanding, you'd say he/she is on your ass all the time. I don't hear ball busting very often at all.