I have fibromyalgia and currently on melatonin, meloxicam, and zoloft (sertraline). Am I ok to take valerian root for sleep and stress?

Probably. Valerian root works on the same brain receptors are valium but is much weaker. The other medications you mention do not crossreact with it. Caution, melatonin can cause abnormal menstrual cycles. I suggest you consult with a reputable naturopathic physician who prescibes appropriate diet, herbs, and supplements. Be careful. The fda regulates these as food and content labeling may be inaccurate.