Thank you for your inquiry. From what we gather from the question, you were asking about the risk of HIV transmission through sharing chapstick.
From the information given, this scenario is deemed to be No Risk (Transmission of HIV is not possible in the given scenario).
The scenario mentioned above does not meet the three components of the transmission equation. It does not satisfy the equation because in order for HIV to be transmitted, blood containing the virus would need direct access to the bloodstream via large open wounds/cuts that were visibly bleeding, (much larger/deeper than chapped lips). HIV needs a very controlled environment to survive and does not reproduce outside of the human host. Even if there was blood present on the chapstick before your daughter used it, once exposed to the air HIV depletes in concentration rapidly (90-99% within several hours), meaning that the risk of transmission would essentially be zero (1).
Recommendation: No need for HIV test with the scenario provided, refer to a healthcare professional for other health related questions
AIDS Vancouver Helpline/Online, Rashell
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1.) Survival of HIV in Environment