Your situation involves personal contact with an object in air ( toothpick 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.
Thank you so much for your answer
Just want to agree that you could never get HIV from such a thing. Does your friend have HIV, first of all? But regardless, you could not get hiv from a stab of a used toothpick. Air inactivates the virus as does saliva. The only ways adults get HIV is from unprotected vaginal or anal sex or sharing IV drug needles. That's it.