Hello Sir,
The situation you described does not carry any risk for infection like
HIV or Hepatitis. Once blood is outside the body and exposed to the environment (floor, carpet, cardboard), viruses cannot survive in a way that can infect another person. Also, you mentioned there was no visible cut or bleeding on your finger — microscopic invisible bleeding does not transmit infection.
So, you don’t need to worry in this case. The irritation you felt is likely due to the sharp edge of the cardboard, not due to infection risk.
I hope it helps you. For more info you can contact me, just go to my profile.