The crate is the only way to go with your pup...she may fuss at the beginning going in...but it will get better soon. Feed her in her crate, so she understands that it's a good thing.
Also give her a command everytime you want her to go in the crate...I usually say "kennel up" and throw in a treat towards the back of the crate...so that the pup will go in quickly.
I am concerned that your 4 month old pup is shy and walks behind you
....a young pup should not be shy. She should be happy to see people and the world. Sounds like all that time she spent outside in her first home she was not getting enough socialization. A scared pup, can soon grow up into a snapping, nervous dog.
Please get her into Puppy Classes asap!! and continue with classes for the next 2-3 years with her.
Also get her out and about in the world, stores, crowds, people...you want her meeting all sorts of kids, adults and different races. Take some treats with you and ask friendly looking people to give her a treat.
Gina