Well yes, traumatic myositis ossificans can be a possibility, even though intercostals spaces (spaces between ribs) is a less common site of its presentation. A chest X-ray should be able to rule this out. Treatment is as you are following—rest, immobilization, ice pack and NSAID.
The other possibility is costochondritis, which causes pain and tenderness at points where your ribs attach to your breastbone. The inflammation around the joint area gives sharp pain on taking a breath. This can also cause tenderness on pressing the area which pains. An orthopedic doctor can diagnose this for you. Generally there is no cause. However it can be due to infection, blow, injury, or fibromyalgia. It usually goes away on its own. Otherwise it can be treated with muscle relaxants, and non steroidal anti inflammatory drugs.
In either case, treatment is usually conservative and spans over weeks before there is proper relief. Take care!