Thank you for your inquiry. From what we gather from the question, you were asking about the possibility of HIV transmission through potentially swallowing spit containing blood. From the information given, this scenario is determined to be No Risk (HIV transmission is not possible in the given scenario).
The reason why there is no risk for HIV transmission in this situation is due to the fact that HIV does not spread through saliva (1). Saliva can "inhibit HIV replication in infected cells and can rapidly kill HIV-infected leukocytes" (2). This is because saliva has "components that can aggregate HIV" and also contains proteins which can protect against HIV and render HIV particles ineffective (e.g. peroxidases). Therefore, even if you had swallowed blood containing HIV particles, it is extremely unlikely for HIV transmission to occur in this situation.
You mentioned that you may have had chapped or mildly bleeding lips. From the HIV Transmission Equation (see below), HIV transmission requires HIV particles in a bodily fluid (e.g. semen, pre-cum, vaginal fluids, etc.) to have direct access to the bloodstream through a High, Low, or Negligible Risk activity. In order for HIV transmission to be possible in this scenario, the transfer of the bloody spit onto the small cuts on your lips would have had to happen in a very close and instantaneous manner to facilitate direct access to your bloodstream, which is not what you described had occurred.
Recommendation: No need for HIV test with the scenario provided, refer to a healthcare professional for other health related questions. Best regards,
AIDS Vancouver Online/Helpline, Shirley
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(1) HIV Transmission Basics
(2) The Oral Mucosa Immune Environment and Oral Transmission of HIV/SIV