Actually, the viral load is at its highest level, often in the millions per milliliter, during primary HIV infection, that is, in the first few weeks after infection. At about the time antibodies appear, the viral load begins to go down until it reaches the set point. Viral load levels at set point are a pretty good indicator of long-term disease progression as well. So if someone has had a potential exposure say, within the last month, a viral load test would show the presence of VERY high amounts of HIV in the blood. The viral load test can occasionally give a false positive, but a low amount (<5,000 copies per ml) usually indicates a false positive. A real positive would have much higher amounts, in the hundreds of thousands or millions.
P24 is not a stand alone test and is good for the first 3 weeks of infection. There would be no reason to get a viral load test this early, you more than likely wouldn't have a VL that is within detectable levels. Viral Load tests are used to monitor the progress of people diagnosed with HIV and to see how their medication is working.
I'm not an expert by any means, but I think your concerns with the blood are well-founded. Not so much because of the blood around the base of your penis, since that would not be a problem unless you had cuts or sores there. But the blood could have gotten in through your urethra. This is exactly what can happen with anal sex. I certainly think you need to get tested, but I don't think you should be overly worried. You are probably OK, since 1) there's no guarantee she's positive, and 2) penetrative pnprotected penile-vaginal intercourse is, while risky, less risky than several other types of sex.
I don't have any data on female sex workers in Thailand. Still, the fact that she'd let you do her without a condom is probably a cause for concern, as it strongly implies that she's let other customers do the same thing. You can't go wrong getting tested at 30, 60, and 90 days. And if you're really in a panic, there are a couple of other tests your doctor can do within a couple of weeks of exposure that could show either p-24 antigens or viral load, if you're really worried and want answers immediately.
You do need to test, for hiv take a 6 week test for a 95% accurate test and then at 3 months for a conclusive result.
You had unprotected sex so you put yourself at risk. You need to test not only for HIV but for other STDs. HIV tests are conclusive at 3 months post exposure. Contact your STD clinic to see when you need to test for them.