Certainly such partial condom failures are rare. But obviously not impossible.
As for the influence of your "minority" status and that of your partner, these factors may elevate the risk. But not necessarily -- geography makes a difference (country; and in the US, east coast inner cities have a lot more HIV than elsewhere), and there is extreme variability within minority groups. African Americans are at highest risk, Latinos lower, Asian-Americans at actually statistically lower risks than whites. The reasons for all this are very complex. Here is a thread that explains some of it, in relation to African Americans, but some of the concepts are similar for other minorities:
http://www.medhelp.org/posts/show/1261996
Turning back to your situation, in the worst case scenario, these factors probably elevate your risk. But even if it were a tenfold difference, the odds remain very strongly in your favor, e.g. with a maximum risk calcuation of 1 chance in 20,000 you have HIV. If I were in your situation, I really wouldn't be worried.