I went on them after I was pregnant with my third. I was on Zoloft.
I suggest calling your OB (or if this is your first, then consult whomever prescribed it) to see if your med is okay. IF it is not, then they can find a different one.
Was going to go on Zoloft anyway as a preemptive measure against PPD, but I got so bad during pregnancy that I did take it while pregnant.
Usually anything you do isn't a problem until an embryo impants. It is at that time that they are gettign what you ingest in some form. Usually a BFP will show up within 6-12 days of implantation. Lots of woman do lots of things without realizing they are pregnant and baby is born healthy. I really wouldn't over concern yourself with it, but in the event of a BFP, consult doc immediately.
Anxiety doesn't go away when pregnant and I wouldn't necessarily want to be off meds if there was a med I could take to avoid that.
You also would not want to quit cold-turkey, ever.