It makes sense with what your doctor is advising. The window period for most finger prick HIV tests is usually 3 months. Its great that the person had a negative result but I can see why your doctor wants to be cautious for a couple of reasons.
The first one is that the window period is 3 months for this type of test which means the person could have had HIV recently passed to them and the test could be negative. This would be called an acute HIV infection and is probably the easiest time to pass HIV to another person because the HIV levels in the body are so high. Odds are she is probably HIV negative but I can see why your doctor would want to take the worst-case scenario for your care.
If you wanted to stop taking PEP you could always talk to your doctor or the person about doing a HIV PCR/NAAT test that actually looks for the virus in the blood.
The other reason your doctor probably wanted you to start PEP is in terms of the person’s risk profile. This person is working in sex work and having unprotected vaginal sex with clients.
It sounds like you are receiving good care from your doctor and I would follow their suggestions on what to do in regard to this concern.
Let us know if you have any other questions or concerns.