What us difference between sprain and fracture of little finger. doc said it is mot fractured but it burns and hurts to bend it even though i exercise?

See specialist: Sprain is a soft tissue injury (muscle, tendon, ligament) vs fracture (bony injury). If you are taking Aspirin products already without relief of pain when/after exercising, you should see a specialist: orthopedic surgeon, sports medicine specialist, chronic pain specialist, or a physiatrist (rehab specialist).

Not much: Really depends on part of bone broke. A bad finger sprain or injury to the knuckle can cause prolonged swelling and loss of motion. Sometimes a soft tissue injury can be worse than a break. Bones heal. Soft tissue can take its sweat time. I would try to focus on icing and early range of motion. If stiffness persists for longer than a couple weeks you probably should see a hand doc.