There are a few possibilities. One is that you do not have a fracture. In this case, your pain is likely due to severe bruising of the bone/ligaments/muscles in the area that can take several weeks to begin to improve. Treatment is with rest and time.
The other, I suspect more likely, possibility is that you do have a fracture. Orthopedists will treat injuries as if they are fractured even if the x-rays are not completely consistent. While most fractures will show up on x-ray some do not. Generally, you would see the calcifications that you are mentioning if there was a fracture but this is not a guarantee. Treatment in this case is rest (using the splint) and time.
Fortunately, which ever the actual case is the treatment is really the same. I would recommend continuing to wear your splint and resting the hand as much as possible.
If your pain is not improving over the next week or so you should follow up with your doctor.
Advice and opinions given are based on the information provided and must not be considered an official medical recommendation. The limitations of the internet prevent an appropriate evaluation. Always consult your doctor if there is concern.