I wouldn't take it to a shelter just because its trying to come inside. It's probably an inside dog, which is how it got hurt.
Its getting cold at night, I wouldn't blame it for trying to come in. Like red said, wash that puppy down and let it in. At the very least put it in your garage if you've got one.
cant risk it with fleas and other baddies, they inevitably have them, not to mention it could have diseases, even from a small amount of time on the street, my dog is vaccinated but I still do not take chances, even a vet will tell you that is not too smart if you want a CLEAN house...and a healthy pet, of which I want both. I am letting it sleep in my storage shed in the mean time to get out of the rain and wind.