When there is a problem with a finger, the hospital "splints" it by taping the the ill finger to the next one, this immobilises and keeps the ill finger straight to allow it to receover. They do the same when there is a problem with a toe as well.
Yogurt and ice as a compress both work because being cold they help to cool the inflamed flesh.
Only an xray would show whether there is any damage to the bone.
You should probably got to a clinic and have them take a look at it or ice it and splint it for a week and see how that feels and if it doesn't help defiantly go to a doctor.
You may have severely bruised the bone, or fractured it by the force that went on the hand as you landed.
An xray of the hand would be able to show whether you have caused damage to the bone.
In the meantime strap the middle finger to the two either side to immobilise it. You can apply a lot of natural yogurt to that part and lightly bandage it. This helps by drawing out the inflammation.
Keep your weight off that hand too until it is fully healed.
Look after your hands, they are delicate instruments (so I was told by a consultant when my tendons were damaged through overuse - rowing a boat).
Best wishes.