NO.
HIV is not transmitted unless you have sex with an infected person or share IV drugs, that's it. Perhaps educating yourself about HIV is a good idea. This is very irrational thinking.
I understand HIV cannot reproduce outside its living host. But I drank out of the water bottle right away. Would it possible the original hiv virus was still alive, if she had hiv and an open cut?
HIV is unable to reproduce outside its living host (unlike many bacteria or fungi, which may do so under suitable conditions), except under laboratory conditions; therefore, it does not spread or maintain infectiousness outside its host.
HIV is transmitted by;
Unprotected penetrative anal and/or vaginal sex
Sharing works with other IV drug users
Mother to child