I've never had a dog class where whistles were used. Are they trying to get the dogs used to noises? That's strange. The problem you are going to get is, as Dante freaks out, whoever is holding him is going to try to comfort him, which is totally the wrong thing to do. That will make it worse, and is probably what is happening.
I would not send him to daycare if that's just going to add stress. And it sounds like it will.
In class, see if you can skip the passing around part, though, at my club, they do that every class. It's a big part of the socialization.
Somebody in my last puppy class had a mini-Ausi that was just terrified of being passed around. He never really improved much by the end.
Now MY Malinois was a total basket case in Puppy Kindergarten. She even managed to slip her collar and get away from one woman. I told her, "You lost her, go get her." I was joking. She's 5 years old now. When there are people around, she wants to stick her nose in their pockets, but backs up when they try to pet her.
Other dogs freak her out. But, other than her little issues, she's great at obedience and agility. She's a good tracker, too, when we have time to practice. I just work with her and keep her out of situations that she finds uncomfortable. So, we often get walks alone together. (Like today.)
She's my early warning dog, because she will bark at the slightest noise in the middle of the night. But not good for staying in motels.
If noise continues to be an issue, something I've found to work really well is to laugh a little and say something really light, like, "Do you hear that! That's somebody being noisy." I really helped with Doerak's and Ciana's noise issues.