You should have moved on from this non event on Feb 28 - considering how many people, including the sw have advised you. Seek therapy instead of continuing to imagine and post about a silly hiv infection idea that no one here will ever believe. hiv science is 40 years old, so you won't convince anyone here that you have made a new discovery about how it is transmitted.
Rest easy, as stated, you're concerns about HIV are unfounded. HIV is not transmitted by the exposure you had. I know your anxious brain keeps you wanting to 'be sure' but that is anxiety. Nothing to do with an actual risk for HIV as you had none. Reassurance seeking is the hallmark of anxious thoughts. The more you seek it either by asking or researching yourself, the more trapped you are by the thought THAT ISN'T REAL. So, try your best to just move on as this was not a risk. Coughs are common and HIV is not.
1) Having unprotected (no condom) penetrative anal or vaginal sex, OR
2) Sharing IV drug equipment with other IV drug users.
No other event that you can think of, including the event you mentioned, puts you at risk for HIV. This is a NO RISK event. You do not need to test for HIV.
No penetration = no risk.