I've been on an anti-depressant for the last 10-12 yrs or so. No change in my hair.
How old are you? Hormone changes can cause changes in your hair too.
My hair didn't get curly until I was 12yo so it could go straight again. (I sure hope not)
I've always used a SNRI. Maybe you can change the type you're using. I use the SNRI for pain and sleep so I have more leeway in playing with it. Is going off the anti-depressant an option? Or switching to another? If it's not, then sadly, you may have to live with the straightening hair.