Whatever you think of prostitutes, most/almost all are aware of the inherent risks in their profession and are out to protect themselves, and insist on consistent condom use with clients. Only a small minority (less than 1%) are infected with HIV. They are at far greater risk from their clients (i.e. you) then their clients are from them.
You didn't need to test the condom with water- when condoms fail they do so catastophically. Anyway, you seem to realize that the condom was intact, but somehow are not grasping the significance of that: HIV cannot be transmitted through an intact condom. Protected sex is just that- PROTECTED.
You had no risk for HIV and do not need testing. If you need additional information/reassurance, please search the forum for hundreds of threads about protected sex with sex workers.
You had no risk here. Put simply, you used a condom, it didn't break (therefore no failure rate there). She also did claim to be HIV negative. Not that going by someone's word is foolproof, but she DID say she had paperwork to prove (most people wouldn't say that unless they can back it up). Getting HIV on a single encounter is a rare occurrence if the person is actually infected from female to male transmission.
If it puts your mind to rest, get tested in three months, but if this is the only situation that is concerning you, I guarantee you that the test will be negative and you will just be wasting your time.
You had protected Sex , move on