My left shoulder was dislocated in 1976 and again in 1985, which resulted in recurrent bouts of bicepital tendinitis. The most effective short-term treatment was ultrasound, but I did not achieve anything permanent in the way of rehabilitation until physiotherapy was made more accessible (when I first got hurt, physiotherapists worked only in hospitals), and non-steroid anti-inflammatory drugs became available in without prescription.

If the doctor at A&E didn't refer you to a physiotherapist, do whatever you have to do to get referred; a good assessment and prompt treatment at this stage will save you -- literally -- years of misery and may save you a permanent deficit in that arm. Think of it as an engineering problem: the inflammation is worsened by the weight of the arm dragging on the injured tissues, but if you immobilize and support the arm until the inflammation subsides, the joint will seize up!