Burning sensation in forearm when recovering from a dislocated shoulder?

I'm not a shoulder/upper limb expert by any means, I am but an Emergency trainee but my explanation would be as follows:

In shoulder dislocation although rare you can damage a nerve called the musculocutaneous nerve which arises from the brachial plexus (around the neck / axilla (armpit). This nerve gives off a division known as the lateral cutaneous nerve of the forearm which gives sensation to the outside of the forearm.

The burning sensation you are experiencing may be neuropathic pain from irritation / damage of this nerve - don't sepair, this often gets better with time.

Perhaps a trial of a pain medication targeting neuropathic pain such as Gabapentin may help, speak to your GP.

Hope this helps

Dr T Miller.