About four days ago, i punched something. now, the 4th and 5th knuckles still appear larger than normal with some stiffness and pain with pressure. is it possible that theymight be broken?

Fracture: A fracture is likely. An x-ray would help make the diagnosis and assist with appropriate treatment.

Fracture Metacarapal: We call them boxers fractures, a "boxer's fracture" occurs as a result of axial loading of the 4th and/or 5th transverse neck of the metacarpal bone secondary to an indirect force such as striking an object with a closed fist

Swelling: Can be associated with fracture or contusion but if you have any sign of skin break such as a cut or small scratch and you could have hit someone in the mouth there can be a very serious infection that needs urgent treatment , these so called fight bite injuries are serious. So for persistent swelling get evaluated even if there is not skin break.

Probably broken: Get and xray from your doctor or urgent care you may need a splint to preserve full function.