Can stomach pain and diarrhea be linked to any stds?

Not usually: Stomach pain and diarrhea are not symptoms usually caused by STD's

Other cause likely: Yes, an STD can cause both lower abdominal pain and diarrhea, especially if it has progressed to a full pelvic infection. More commonly, one would expect vaginal discharge, menstrual cramp like pain, or pain with sex. More likely cause of abdominal pain and diarrhea is an intestinal infection of some sort, usually viral or food borne bacteria, but IBS and IBD can also cause these symptoms.