Trying to follow your post. You were pricked by a needle that had been used by someone else? Why? By accident? Normally that isn't something that a health care provider would do. However, it is not a risk for HIV as you seem to be aware. Needles that are lancet needles simply stick us and are exposed to air which you seem to know renders the virus inactive. So, that needle stick was not a risk. The only risks for HIV are unprotected vaginal or anal sex or sharing IV drug needles. I have no idea what you are talking about too with the window period of 10 to 15 days (obviously wrong) but woudn't matter if you had no risk to begin with.
Your situation involves personal contact with an object in air (lancet 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.
If hiv was as infectious as you are worrying about, we (and that includes all children) would all have it by now, just from touching infected people when we both have cuts and their belongings etc. You said you know hiv can't live in air and it was 15 seconds so you already explained it was dead, so you should move on from hiv.