STDs are not transmitted by hand to genital contact. It simply does not occur.
Your second paragraph is insightful and basically correct. You cannot rely on vague symptoms indicating infection. There is no way you acquired an STD from that exposure, and your symptoms are not those of any known STD anyway. As I have said innumerable times on this and the HIV forum, when somebody suggests his or her own symptoms likely have a psychological origina, s/he probably is almost always right.
Good luck-- HHH, MD
HHH, MD