You asked her if she was talking about you to others behind your back, she said no.

She lied.

You're not in the wrong at all, she's lying to you, betraying your trust and disrespecting you.

Dunno, if you can't trust this woman to exercise some self control and not use you as a gossiping piece, then there's a decent chance that down the line she could demonstrate the same lack of self control and morals and cheat on you, and neatly cover it up with her habit of lying.

Not sure if you're married or what but I'd start thinking about things between you two if I was you.

She's in the wrong, all you did was type a mean message over text as a response. She's currently stabbing you in the back.

Might not be the most moral thing to do but maybe start talking to other women, maybe you'll be lucky enough to find one who isn't a Judas.