Sorry to hear about your wrist. Having had various injuries from falls of bikes and such, I know that they can be quite painful and sore for some time.
Sometimes, your initial X-ray might appear normal, but later images may demonstrate subtle breaks in bones such as a the scaphoid. The doctor that you spoke to is also correct in that you may have sustained a ligament injury, but there might also be an element of bone bruising (swelling in the bones themselves) - from experience with other patients, this can take several months to settle.
If you are having pain and limitation in movement, it may be worthwhile considering further clinical assessment. Depending on the assessment, it maybe that a repeat X-ray or ultrasound examination of the wrist is required. Treatments could include splinting, oral analgesia, prolotherapy injections (for ligament injuries) or surgical intervention for fractures.
I would suggest visiting a Sports/MSK physician in the first instance for a more thorough clinical assessment/further investigations, but if you happen to know a physiotherapist, this might also be an option.
Sorry to hear about your wrist and I hope things improve soon.
BW
Dr Dinesh
