Firstly -What is the mechanism of injury ?
Next - kindly mention if there's any swelling in that area !
Any other associated symptoms like breathing difficulty? , restriction in movements
Soft tissue injury and rib injuries are possible from what you are describing. And they can take months to heal based on individuals healing capacity.
Next Steps
as your doctor has suggested CT scan will help diagnose in case of any bony injuries or lung contusions.. other soft tissue injuries are much better diagnosed on MRI .. but is unnecessary at this time.
A USG scan of soft tissue in the area may give clue regarding any hematomas in the area.
Health Tips
don't over think! some people genuinely require higher time to heal.. soft tissue injuries take 3 to 6 months or more to heal sometimes.. it could absolutely be normal ..
any increase in pain or change in nature of pain , increasing swelling, breathing difficulty warrants an immediate consultation in your nearest emergency .