I think it is more likely that the sex worker had a cold and has passed it on to you, a dry cough would also be part of a cold so that fits in with the assumption too.
However, I have to ask, why would you have unprotected sex with someone who sleeps with countless men?
It's worse still that she allowed it, because if she was willing to have unprotected sex with you; she is probably doing it with everyone without a condom. Though frankly, this is generally unheard of in that industry!
You do need to get tested as soon as possible. HIV is not the only thing she may have passed on to you, and some sexually transmitted diseases affect fertility and can be very unpleasant.
The symptoms of HIV tend to start around ten days after the infection enters your body, so the cold like symptoms you describe as having the following day were unlikely to be an indication.
Get tested as soon as possible though, so that if you do test positive for HIV you can protect yourself and others. Whether or not you have this disease, please always use protection when having sex with someone you don't know, especially when your sexual partner has unprotected intercourse for a living!