You have a couple of issues here.
1. Socializing is NOT immersing your dog in whatever they are worried about. A reactive dog should have obedience, not forced to play with others. Socializing is letting them experience and watch the world while you guide them through. So, NO, I would not put a puppy who was reactive at such a young age in day care for that reason. I would, and have, worked on it differently. But that's for another thread.
2. No day care is going to allow an unvaccinated puppy into their facility. They will not risk the other dogs.
3. If your puppy catches parvo or distemper, because the last vaccination is at 16 weeks, and dies then socializing is a moot point.
So the answer is....there really isn't a choice here. You don't risk your puppy's life.
Find a safe place, with dogs you know have a good temperament and are vaccinated, AND in an environment you control. Maybe post a location on here and someone here could help you? Or call a local AKC club and see what options they have for you as far as group classes (again, they will want your puppy fully vaccinated)
In my experience, your puppy doesn't need to be immersed in other dogs. She needs to be told No. Been there, done that.
Right now, work on obedience. Teach her Sit and Look At That. That will be more of a benefit to her when you are able to go out so she understands that being a whirling dervish whenever another dog goes by is not allowed.