Yes
HPV can cause cervical cancer in women. It usually shows up as genital warts, but can lie dormant and not show any symptoms for quite a while, so it's really hard to tell if you have it. And there is no test for men. However, there is a vaccine that protects women against the types that most commonly cause cervical cancer- if they have it in your country (Gardisil) it might be worth your gf getting it (regardless of the prostitute thing- it's just good to have)
Chlamydia can also cause serious damage to a woman's reproductive system- and is often present without symptoms. However, there's a pretty easy test for it. I'd recommend you get tested.
Gonorrhea is also an easy one to get tested for and might not show any symptoms- but it doesn't always show up on a test until about 30 days after infection.
Watch for herpes as well- but you would probably have an outbreak by now if you had that (sores in your genital area)
Syphilis- also usually shows as a sore. There's a blood test for it.
Bacterial infections: it would probably be obvious by now if you had one (discharge from your penis)
Most of these std's can lead to worse problems in women- PID- (Pelvic inflammatory disease) which can cause a woman's reproductive system serious damage or even infertility. Which is why it's important that you get yourself the full run of tests. I'm not sure if it would be necessary to test for all of these. Chlamydia and gonorrhea are really easy and common tests.
But like someone said above- you used a condom. So although these are all possibilities, it's not all that likely. If I were you, I'd just let a doc know what you did and the doc will know what tests you should do. And don't be embarrassed, it's a lot more common thann you think! People make mistakes.