It is sad that your puppy is hurt, but I agree with Dr. Humphries, ownership of a puppy means that there is a responsibility for all kinds of preventative pet care such as vaccines, deworming, and spaying, not to mention care of injuries. There is no need to put her down, you can contact a beagle rescue group who can try to find a person to adopt Dott and pay for the care that she needs. A rescue group that serves Indiana is RobDars Houndsong Rescue: http://home.comcast.net/~robdars/robdar2.htm
Kimberly Coyner, DVM DACVD
Sorry we cannot do emergency care here. She needs to see a veterinarian.
This could be a injury of any kind, not necessarily a dislocated shoulder. It will take an exam to determine what is wrong and how it is treated. Many vets have a Care Credit system where you can pay over time. But what are your options? A 8 or 9 week puppy also needs vaccinations, spay, heartworm prevention, as well as sickness and injury care. Pet ownership is such a responsibility and you must plan for it.
good luck.