if you want to get tested for HIV...chances of transmission are extremely slim even with the break...you have to wait at least six weeks to take a blood test that will be 99 percent reliable, then take a test again three months after the incident.
The virus is difficult to pass, especially to the male in M/F anal (assuming you are the male and were having anal with a female escort.) Also, the condom protected you till it broke, and you likely pulled out quickly.
Not sure what to tell you about other STDs, but you didn't contract HIV even on the very slim chance the escort was HIV-positive. Someone may tell you that you can get an emergency prescription for PEP, which is taking a regimen of AIDS drugs for 36 days in an attempt to kill the virus. This works sometimes in very high risk cases such as a "bottom" who has onprotected anal sex with a known HIV-positive male. But your encounter was very low risk for passing the virus even if the woman was infected with HIV, which is very unlikely. The odds of transmitting the virus in that high-risk scenario are estimated to be 3 in 10,000. So the odds of you getting it from an SP who is almost certainly not infected? Nil. Still worth testing if it puts your mind at ease. (my expertise: worked as an HIV volunteer counselor at a clinic) Also, re PEP: it is too late.Need to get it within about 36 hours. And you don't need it.