Can hepatitis b pass thru expired rubbing alcohol?

my grandfather had hepatitis b and severely and died from it. three days after he died we went to to clean out his apt... and i had a cut so i used his bottle of rubbing alcohol and poured it over my cut. then almost instanilty i noticed what i just done and became parionod so i looked at the alcohol bottle and noticed it was expied like in 08 or something and then i saw stuff floating like little black lint or something can i have hepatitis b now? i am super duper scared!