Grammy's point is that puppies this young should not be biting hard enough out of frustration to draw blood. If she had been properly socialized at the breeder's, she should've learned a bit of bite inhibition, in which case she'd be nipping you but not hard enough to "draw alot of blood" as you say.
There is an assumption here that the puppy is biting to protest the picking up. That was not at all my first assumption, maybe bc I have working dogs. I have seen many puppies that get excited and bite playfully as soon as you get near them. They are not trying to hurt you, they are just too excited and haven't learned the limits on biting. If the mother and breeder and litter mates didn't teach it, then it's your job. No biggie. (However, if you think she is biting to make you stop handling her, then this is a totally different problem and needs to be dealt with very differently)
Another thing- all of the older clients I ever worked with had this problem to some extent. As you age, your skin gets thinner and more delicate so that normal puppy biting does damage that it would not do to younger skin. So, I'd need to know your age before I'd be shocked that the pup is bloodying your arms.
You've already tried the screaming, which will often work on sensitive, compliant pups. It doesn't work well on tough breeds that have been bred to bite and ignore the screaming. Standard schnauzers are very tough dogs and have been bred for protection work. One alternative is ignoring the puppy, but you'll find this is very hard to do while they are hanging on your arm. You can try to prevent the problem- make sure your arms move nice and slowly and you never jerk them away when she tries to bite- that only makes you more fun to chase.
But when she actually bites, she is rewarding herself and you need to have a way to make it not rewarding for her, or this problem will not go away- biting is just too much fun for a drivey dog. I have had a lot of success with very calm, non-confrontation corrections. If she actually bites you, make sure you do not pull that arm away- that just makes it more fun for her. Hold your arm totally still (you may need to wrap your arms for a while or wear a jacket around her so this doesn't hurt) and reach under her chin with your free hand- nice and easy so she doesn't see it coming. Use that hand to grasp some of the loose skin around her neck and pull her into the bite (not away, which will be your instinct).
Pulling her into the bite is exactly the opposite of what is fun for a pup. She will feel uncomfortable and you will hold her here, tight and firm until you can see her mood change. At that point, she will try to get away from you (a total 180 degree change of mood). I usually hold them a couple seconds longer and then let them go. Make sure you do not move your arms around as you let them go- keep them right where they were. If she tries to bite again, let her and then use your free hand to correct again and hold her a little longer when she wants to go to make the experience that much more unpleasant.
Each time she lets go and backs off, praise her very calmly, but don't try to pet her (any arm movement will excite her and make her want to bite). If she approaches you sweetly, then you can pet her, but make sure you keep all your movements very slow and easy and only pet her from underneath until this problem is resolved. Petting along the top or sides of the head tends to incite the biting, as does rough or fast petting, so make sure you move in slow motion until you have no more problems with this.