I think I broke my 5th metacarpal. How can I be sure without going to the hospital?

Urgent care. Most urgent care centers have xray machines and the ability to get you in and out pretty quickly and at reasonable expense.
Metacarpal fracture. Other than pain, tenderness, and deformity, if you try to make a fist and your fingers scissor over each other, that is one sign of metacarpal fracture but the best way is to obtain and x-ray.