I agree completely with monkeyflower, who responded before me (below). There is no risk here, and anyway, the odds that any particular 19 year old woman in New York has HIV is close to zero, especially if she isn't from an AIDS-endemic country and not an injection drug user.
HIV is a rare cause of the symptoms you describe, compared to innumerable other conditions--and most of the symptoms don't suggest HIV anyway. 'Groin nodes seem to be swollen' doesn't count unless lymph node inflammation is confirmed by a health professional; and absence of fever rules out HIV. Your only health problem undoubtedly is your stress/depression over the event, which are entirely unwarranted.
Mellow out; you're fine. But if your anxieties are not settled by this reassurance, have an HIV test if the negative result will help resolve your fears.
HHH, MD
There is no symptom that is unique to ARS. All symptoms of ARS, including the rash, enlarged lymph nodes, etc, are identical to those of other conditions that are more common than ARS.
I don't guarantee anybody is free of HIV. But you came to this site seeking my expert opinion and, presumably, reassurance. Get tested if you feel like it, but in the meantime accept the good news and stop trying to talk me into agreeing with your fears.