Thank you for your inquiry. From what we gather from the question, you were asking about the possibility of HIV transmission through an unknown fluid entering your eyes. From the information given, this scenario is determined to be No Risk (transmission of HIV is not possible in the given scenario).
The reason why there is not a risk of HIV transmission associated with this scenario is due to the fact that it is extremely unlikely for there to be fresh bodily fluid (such as blood) dripping from a ceiling in a setting such as a grocery store. Furthermore, as you alluded to in your question, when HIV outside of the body (contained in a body fluid like blood) is exposed to oxygen, this causes a rapid reduction in HIV concentration (1). From the CDC, HIV outside of the body that is drying on a surface, has a rapid (within several hours) reduction in HIV concentration of 90-99% (1).
A higher risk assessment may be present in circumstances where fresh blood from another individual theoretically enters another individual's eye instantly (i.e,. without having an opportunity to dry out on a surface). In these circumstances, the reason why HIV transmission may be possible is due to the HIV Transmission Equation (see image below), which states that HIV transmission requires a bodily fluid (e.g. blood) that has direct access to the bloodstream (e.g. via open cuts and sores, sexual organs, mucosal membranes, etc.) through an High/Low/Negligible activity. In this case, blood from an HIV positive individual could theoretically have direct access to another individual's bloodstream through the mucous membranes in the latter's eyes.
Recommendation: No need for an HIV test with the scenario provided, refer to a healthcare professional for other health-related questions.
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1) HIV Environmental Exposure