Caring for a Puppy With Parvo?

My 4 month old Sharpbull (cross between Shar Pei and Pit Bull) puppy was just diagnosed with parvo today. He started acting funny late night on Wednesday and today, Friday, was vomiting bright yellow and just laying around not eating. We took him to the vet and he has parvo and worms. They gave him an antibiotic shot and worm medicine and sent us home with IV and other med. He has been on the IV for about 9 hours, off and on, like they said.

He went to the bathroom outside, but he just urinated. He has never had diarrhea. While he was out in the yard he ran and I mean ran over to his outside water and gulped down a few licks and then proceeded to bark at the neighbor. When we brought him back inside it was about an hour later and then he started to vomit the bile again. But now it is a light milky color not bright yellow anymore.

Am I doing this right or is he getting worse? I am so confused since I didn't get to go to the vet with him. My daughter and husband did and I am not sure they are to up on what is all going on. They were too upset and I have to go back in the morning to get another bag of fluids. If I am doing right should I be letting him run and drink if he wants to? I didn't tell him to he just did and my daughter said he was barking at a dog twice his size at the vet. Any help on this would be greatly appreciated.