Please do seek professional care as soon as possible. Dogs have nerves in their tails - an injury can be really painful, although dogs (like most other animals) instinctively hide their pain.

I don't want to scare you but I know a dog and a cat who both died after tail injuries and one of my neighbors owns a cat whose tail was permanently injured (and the cat barely survived) after someone viciously lifted the cat by its tail and swung it around.

An animal's tail is generally considered a barometer, so to speak, that indicates their response to every sight, sound, fear, excitement, etc. It's all about nerves and injured nerves are painful.