I am glad you brought her home.
Gemy has given you some good advice. The first thing is find a good vet and take her in for a good assessment.
Get her and your other dogs on a good diet. I use 1/4 cup good kibble per dog twice a day but, I do cook for my dogs too and that is the bulk of their food. I consider the kibble their crunchy stuff.
Usually exercise will make her less hyper. Play is good for bonding and training too.
I think each dog needs their own crate, food and water bowls and even some special toys and blanket is a good thing. (My babies each have their own Kong for chewing and treats).
The less hair on the nose thing, should be checked by the Vet. Could be bad hair cut, skin problems, or a dozen other things. You vet can start her on a wellness plan of shots up to date, worm, heart worm, and flea preventive and tests to assess any health problems the Vet thinks might be going on.
Best wishes and welcome to YT.