Why do muscles swell after a minor or a major hand fracture?

Bleeding. Bone actually bleed when injured! so bleeding will cause swelling. Also, injured parts leak water. That's called "edema".
Pain with pushing . The palm ahaist surfaces, called pillar pain is common and can take 2/3 of a year to go away. Pain at rest could be due to inadequate release or may be first sign of infection. Rarely, complex regional pain syndrome.