Your situation involves personal contact with an object in air (floor, toilet etc. 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 driving yourself crazy as the reality is this is zero risk. The only ways you could get HIV is to have unprotected vaginal or anal intercourse or share IV drug needles. Cleaning around a toilet is not a risk. At all. Ever. So, if you have anxiety in general, then it's time to do something about that. Otherwise, you should be able to accept the fact that you don't get HIV from touching urine or anything as air inactivates the virus.
HIV can't be transmitted outside of it's host. Once infected fluid establishes contact with environment, it loses it's ability to infect.
You need to keep in mind that in adults below are the only circumstances that could put you at risk for HIV transmission.
- Unprotected vaginal or anal intercourse.
- Sharing needle to inject drugs with other people.
You event could certainly expose you to other viruses and other microbial infection. However; HIV, definitely is not the concern.