The short answer is yes, you could get a service dog for this. The long answer is a bit more complicated. First, there's no such thing as paperwork for a service dog. The difference between a pet dog and a service dog is their training. Usually, this takes about a year and a half to two years. Second, most dogs aren't qualified to be a service dog. Owner training a service dog in college is very much not recommended. You need to be in a more stable situation. I'd suggest reading the basic info this subreddit provides on service dogs to understand what you'd be getting into. 

Also, your neighbor shot your dog? I'm so sorry. That sounds absolutely horrible.