Thank you for consulting with Doctor spring. I understand that you have injured your chest a few days back and you find it difficult to breathe. Firstly is want to requestion yourself if you had chest pain and shortness of breath before hitting yourself on your snow mobile. If the pain appeared only after hitting yourself the most likely cause is either a bruised or a broken rib.
The symptoms of a bruised or a broken rib include tenderness over the area of the broken rib, pain on taking a deep inspiration, discolored skin over the area of injury; your doctor can feel a discontinuity over your rib if it is broken.
I suggest you visit your doctor as soon as possible. He will want to examine your chest and listen for lung sounds and ensure that there is no air leak. The preliminary investigation to rule out a rib fracture would be to take a Chest X-ray. If necessary and if indicated, your doctor may opt for a Computed Tomography of your chest.
The main complication of severe chest injury, which is unlikely in your case since you have managed without going to a doctor for a few days now is chest infection due to inability to breathe deeply enough. Your doctor may opt to treat you with a Non Steroidal Analgesic like Paracetamol or Ibuprofen if your pain is not too bad or Opioids may be prescribed for better pain relief. Previously it was believed that taping the injured area helps in pain relief but this is no longer done. You may have some residual pain for about a month which the duration required for the rib to heal.