STDs don't cause cough and rarely cause sore throat. Your and your partner's symptoms are much more likely due to a garden variety respiratory virus, probably caught in the usual way--kissing, sharing drinking glasses, etc. Certainly it is possible you were originally infected during your casual sexual encounter, but not by sex per se.
However, there is a group of viruses called adenovirus. Most strains are just garden variety cold viruses. But some strains infect the genitals and can be passed by oral sex, causing simultaneous genital and cold symptoms. Adenovirus ususally shows up as a cough, and conjunctivitis (pink-eye) often is present as well. Adenovirus from oral sex explains 2-5% of cases of nongonococcal urethritis (NGU) in men, so this is pretty uncommon. It probably can affect female genitals as well, but this has never been studied or documented. So conceivably you and your partners are sharing an adenovirus infection. But even if you are, it could just as well have been passed by kissing, and you could have infected your boyfriend by oral sex--but you could do that with an adenovirus you caught as a cold.
Bottom line: Sit tight, and expect everybody's symptoms to clear up on their own. If they don't, see a health care provider. But most likely none of this has much to do with your January sexual exposure.
Good luck-- HHH, MD