i had a bad moment at work today

today i overheard my coworker talking about me behind my back and it really got to me. i started feeling all sorts of negative emotions like jealousy, insecurity, and even anger. so when she asked if i wanted to grab lunch together after work, i just said no and pretended everything was fine. but later on in the shift, i ended up telling another coworker about what i heard, which wasn't really fair to my first coworker who didn’t know that others had overheard her either. now i’m wondering if it’s normal to let stuff like this get under your skin and then lash out at people? or should i just stay silent and try to figure things out on my own without involving anyone else?