Cephalexin (Keflex) isn't the first choice for any STD, but in the usual dose would prevent or treat gonorrhea or syphilis. It has no effect against chlamydia, and no antibiotic is effective against herpes or other viral infections.
You almost certainly had a viral infection, not an STD and probably unrelated to the sexual exposure you describe--except that you could have caught a cold from her. Your doctor should have known better than to prescribe an antibiotic in that circumstance.
You don't need any further treatment, and I wouldn't worry about passing anything on to your new partner.
Good luck-- HHH, MD