One month ago, I was changing my house keys and I was using a used screwdriver that I borrowed from the same local tool shop where I bought the keys. I am not sure if the shop owner usually lends it to people, but he seemed gentle and gave it to me because I didn’t have one. The distance from the shop to my house is 5-10 min away. Once I reached home, I changed the keys but while pushing, my hand slipped and the screwdriver hit the palm of my other hand, making a small cut in the skin with a little blood, which I washed immediately and then sanitised in the pharmacy after 20 min. I don’t recall that there was anything on the screwdriver, but if I assumed that the guy who lent me this tool was positive hiv or hepatitis, and has cut him self accidentally before he lends me the screwdriver, Is there any risk of having HIV or hepatitis from the cut I had? 

The event you describe did not put you at risk for acquisition of HIV or any other blood borne infection.  There are several reasons I say this.  

1.  It is statistically unlikely that the man you obtained the screwdriver, or anyone who used it previously has HIV.

2. Even if it was contaminated by a person who had HIV, HIV is not transmitted through punctures of the sort you describe. The virus dies quickly on exposure to the environment and is non-infectious virtually immediately from the time it is exposed.  

3.  Puncture wounds of the sort you describe are not known to transmit HIV. 

In summary, there is no reason for concern, no reason for testing.  I hope the information I have provided is helpful.  EWH

So if my understanding is correct I don’t need to worry about hepatitis also or test for it, right?

Last comments promise:) 

1) hepatitis virus dies when exposed to environment? Assuming it was there. 

2) the cut I had was less than half CM deep, this is considered puncture wounds? 

This is a puncture wound however puncture wounds of this sort do not lead to infection.,  Puncture wounds with hollow needles, which can "hide" and therefore transfer blood are the worrisome wounds, not wounds of this sort.

This completes this thread

Please don't worry.  EWG