Your situation involves personal contact with an object in air and in saliva (her mouth which is full of air and saliva) which is not a risk for hiv. No worries, because you can't get hiv from personal contact except unprotected penetrating vaginal or anal, neither of which you did and you didn't share hollow needles to inject with which is the only other way to acquire hiv. Analysis of large numbers of infected people over the 40 years of hiv history has proven that people don't get hiv in the way you are worried is a risk.
HIV is a fragile virus in air or saliva and is effectively instantly dead in either air or saliva so the worst that could happen is dead virus rubbed you, and obviously anything which is dead cannot live again so you are good. Blood and cuts would not be relevant in your situation since the hiv has become effectively dead, so you don't have to worry about them to be sure that you are safe.
Yes, you are having irrational anxiety over this. You can not get HIV from a door handle. Air and saliva inactivate the virus and anyone touches will be exposed to air. Therefore, HIV is not transmitted this way. The only ways adults get HIV is from unprotected vaginal or anal sex (with penetration) or sharing IV drug needles. So, no risk here.
If you use the search function here on this website, you will be surprised to see, there are several people who had a similar scare and no one ever has contracted this virus in that fashion. Fact of the matter is; professionals in healthcare are trained to take care of your health and not jeopardize it. Nonetheless, your thought is irrational, it is driven by fear of this disease. Perhaps a therapist will be able to help you to find out the root cause of such fear and help you overcome it.