If the ring and pinky fingers can't bend. does this sound like a broken hand?

Stiffness fingers: Can be from arthritis, muscle weakness, tendon injury, joint stiffness, tendonitis and tenosynovitis, infection, neurlogical causes and other reasons. If this is a new issue or something that is progressing seek an evaluation. In fact even if it is old and you just want to be sure to have a diagnosis , seek treatment as some things such as tendon rupture or nerve issues can be progressive.