I was recently in the hospital to check and make sure I didn't have serotonin syndrome. They told me to stop taking the antidepressants. Is that safe?

Antidepressants can. Antidepressants can cause teh hyperserotinin syndrome. If this is your case your physiciasn can drop the dosage or if necessary stop it. This is something you need to discuss with your physician because I agree with your hesitation and you need to be certain that there is a plan for your depression therapy.
Yes. Serotonin syndrome is a serious matter and any antidepressant med that affects serotonin must be stopped immediately. If you don't have the syndrome you still can stop your meds but check with your doctor because some e.g, Prozac, (fluoxetine) can be stopped immediately while with others it's best to taper down the dose over a few days.