I'd see if he got a rabies shot, if you don't know the dog. He won't give anything to you but the dog might give something to him.
Yea...i have no idea what you could possibly contract from your brother having a dog bite. I dont think you could contract anything actually. You should be helping him recover and not worrying about something that isn't even possible.
The answer to your question is no, you will not contract anything.
What, exactly, are you afraid of catching?
Rabies? Worms? Dog breath?
I find it rather sad you're more concerned for yourself than your brother.