Rabies and vaccination. Site (leg) ?.

I got a street dog bite. It was a scratch without bleeding. I washed the bitten site (leg) under running tap water for 10-30 seconds. And got intradermal antirabies vaccine after 45 minutes. My questions are as follows. Will I get rabies as I did not wash the bitten site with soap for 15 min ?. Can my family members catch rabies because, they wash utensils where I washed the bitten site (leg) ?. I don't think the hospital people maintained proper cold chain vaccine storage method (I am not sure but I think they take out the vaccine out of cold storage at around 10 am and use it till 4.30 pm, in between they may not cold store it) and I got the first dose of vaccine at around 4.30 ( 45 min after being bitten) so, the vaccine might not had cold stored. But, I got the second dose ( 4 th day after being bitten ) immediately after the vaccine removed from cold storage but, they keep the cold storage box always open. Can I get rabies because of this. Kindly clarify me.