I fell on my shoulder, and felt the pain later when i raised my arm. it is a sharp and central pain right in the groove of the joint. maybe a tear?

Possible: Depending upon the time of injury, it should show with swelling or redness besides the local tenderness that you describe if it had accompanying fractire or dislocation. A plain Xray will be helpful as an initial study at an urgent car center and an arm sling for comfort as indicated. You may benefit from PT, which may require a referral. Feel better!