Ok, I got here.
Couple things, honestly, I wouldn't give him breast milk, just like cows milk isn't the perfect thing for a human baby, human breast milk isn't the perfect thing for a puppy. It can cure a lot of things in the species it's meant to feed, but at this point any kind of dairy may throw him over the edge. You could try to get puppy formula though, most pet food stores sell it however, if he were my puppy, this is what I'd do.
First, call your vet first thing in the morning and ask him for sub q fluids, if you aren't queasy, they're easy to do yourself at home (you need to stick a fairly large needle under his skin and then run a bag of fluids fairly quickly) sub q fluids work far better in cats than in dogs and many may say they make no difference in a dog, but they are a definite "can't hurt, might help" If puppy has made it through the night, the vet should have no trouble helping you set that up.
Get the pedialyte into him constantly, but also try some gatoraide, only because it has some sugar which may well help him right now. Actual electrolyte solutions made for dogs do contain sugar (and gatoraide is cheaper!) I would also up the amount you're doing, if you're willing to do it, give him 5 mils every 10 minutes. If he's keeping that down the majority of time, up it to 10 mls every 15 min. For tonight, keep him without food and just the liquids, then tomorrow when you talk to your vet ask him for a couple cans of A/D--I have no use for Hill's pet nutrition, but this is a HIGH calorie slurry type food you can feed with a syringe or off your fingers--also, most animals do like it. If he doesn't have any, don't worry too too much but do get some baby food. In the beginning, just use the straight meat types and you can make him some rice pablum cereal (just make sure it's not the kind that has formula in it-and make it with just water--or unflavoured pedialyte) I would try those two things to get some food into him tomorrow, give it warmed but not hot and offer tiny amounts (like no more than a tablespoon at once) every hour. If at the middle of the day he's eating and keeping it down, up the amount to 2 tbsps every hour or 90 min.
Ultimately, the key is not to let him get dehydrated, that is the absolute most important thing-so if feeding him makes him less likely to drink, forget about the food. You can tell if he's dehydrated by taking his skin at the back of his neck and twisting it a bit, if it stays twisted he's dehydrated. Whether his nose is wet or not doesn't actually tell you much, however, put your finger in his mouth, if his gums or cheeks are dry, he's dehydrated. You can also make sure he's not loosing too much blood into his bowels by pressing the gum area directly above his fang, it will go white but should pink back up again in less than 3 seconds.
Honestly, textbook wise the only way he should make it is if he's on fluids at the vet, but like your instinct is saying, I've seen WAY more dogs beat parvo who had owners willing to sit up all night cuddling and syringing fluids into them than success stories where they were left at the vet. Go with your gut mama, cuddle him, sling him and keep those fluids going in. My guess is that your vet didn't think he'd make it the night, but from the amount you say he's throwing up, I think he has a good chance of still being here in the morning--then push your vet to help you do more for him.
I PM'd you my phone #, I'm up until 11 ish and it 's almost 9 now, if you need more info pleas don't hesitate to call. I'll check back for an update before I go to bed.