Thanks for all the additional information.
This was a quite high risk exposure. HIV is 10-20 times more common in African Americans than in whites, and urban Maryland and DC are among the places with the highest rates of all in AA populations. A sex worker who picks up people in public places (street, buses, bars, etc) is probably at especially high risk.
As noted above, HIV is transmitted less than one time in a thousand from a single episode of unprotected sex, even if the woman has HIV. And the brief period of exposure after the condom broke is strongly in your favor.
Still, many experts would prescribe post-exposure prophylaxis (PEP) in this situation, i.e. treatment with anti-HIV drugs to further reduce the chance of infection. However, to be effective, PEP ideally is started within a day or two, and is not likely to be effective if more than 72 hours have passed. You don't say when this event occurred, but if under 72 hr ago, you should immediately visit a clinic or doctor with experience in STD/HIV prevention. Your local health department STD clinic would be a good option (the Baltimore City health dept clinic is excellent); or Johns Hopkins Medical Center or other academic center; or DC's Whitman Walker Clinic would all be excellent options for this.
Don't panic. While this isn't the news you wanted to hear, the odds are very high you weren't infected and perhaps not even exposed. But better safe than sorry!
Another option, if you are able to identify and contact the sex worker, is to ask her to be (re) tested; you could go together to the same clinic. If you both have negative tests at this time, you can both stop worrying about it.
In case you are interested in more discussion of HIV in African Americans, including explanation of the reasons for it, see the threads below. You can find still others by searching for "African American" in this forum.
http://www.medhelp.org/posts/show/1261996
http://www.medhelp.org/posts/show/717093
I'll be interested to hear the outcome after you have been professionally evaluated.