Not cold and flu specifically but some can make you feel generally unwell. If in doubt, get tested. People that are not monogomous should be tested regularly as a matter of routine and its nothing to be ashamed of. Even if condoms are used, hand-genital contact can transmit some stds especially hpv (genital warts).
Im Sorry to say but HIV does. Within first month of transmission common symptoms are cold and flu like symptoms, hopefully you are fine tho, and its just a coincidence. You're probably a bit run down, make sure you use protection in future.
Don't try to figure it out on your own, you are only going to make yourself a wreck. I just got tested for everything several months ago, and I was reading all about STD's and before I knew I had every symptom of every disease in the universe. A month later I got my test results back......and I was totally healthy. My mind played terrible tricks on me, and caused a lot of unecessary anxiety.