The delay between getting something and you testing positive for it varies according to what it is. For the bacterial ones like chlamydia, gonorrhoea, and syphilis it will often show up immediately given a decent test* and should definitely be found after a week or two.
For HIV, they may well talk about three months, but they should be using a test that will 'nearly always' show the correct result after a month. Depending on just where you go and how much you pay, you can get a test that will do so after a week - that one looks for the virus directly rather than for antibodies to it.
They may want you to test again after three months, again to be sure and to get more money, but the good news is that for receptive vaginal sex, if he was HIV+, it would be about a two in a thousand chance of being infected.
I don't think there's the evidence for the window period for other virals, like HepB.
* i.e. them testing you where you think you might have been infected with a modern testing kit.