Thank you for your inquiry. From what we gather from the question, you were asking about the possibility of HIV transmission through a cut on your hand potentially coming into contact with blood from another individual. From the information provided, this scenario is determined to be No Risk (HIV transmission is not possible in the given scenario).
HIV (contained in a body fluid such as blood) is extremely sensitive to the outer environment. Exposure to oxygen in an environment outside of the body causes HIV to undergo a rapid reduction in concentration (1). From the CDC, HIV that may be contained in a fluid (in this case the potential blood on your car), has a rapid (within several hours) reduction in concentration of 90-99% (1). In other words, even if blood from the woman did indeed come into contact with your hand (via your car handle), the simple fact that it was exposed to oxygen will negate the possibility of HIV transmission in this scenario.
Furthermore, small superficial cuts are not deep enough to permit direct access of blood into your bloodstream, a necessary component of the HIV Transmission Equation (see image below).
Recommendation: No need for an HIV test with the scenario provided, refer to a healthcare professional for other health-related questions.All the best,
AIDS Vancouver Online/Helpline, Shirley
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(1) HIV Environmental Exposure