Consult a orthopedic doctor
Based on your symptoms, it is possible that you may have a pinched nerve or another issue in the shoulder or upper arm area. It's important to seek medical attention to get a proper diagnosis and treatment plan. In the meantime, consider modifying your gym routine and desk work to avoid aggravating the affected area. Be sure to discuss any previous neck spasms with your doctor, as it may be related to your current symptoms.
Hello~I strongly suggest that you see a chiropractor. You probably have some misplaced vertebrae that are pressing on some nerves causing these issues. The chiro will take some x-rays, study them and then go over the results and a plan for your healing. After a few treatments you should start to feel better.
That spot is notorious for tendinitis or bursitis. Repetitive movement that puts pressure on the bursae is common. The bursae can become inflamed. Does ibuprofen take the pain away at all? Have you had an x ray or any imaging of the area? Pinched nerves are always a possibility too. My husband had pain a lot like you describe. He say a neurologist who suggested surgery. You know what was happening? He was using our old mower that the push forward part had broken so it was a lot of work to push and it jarred him over and over. He was going to have the surgery but waiting for winter. But it got better. He didn't have the surgery, and in spring we got the mower out and it started again. We got a new mower and he hasn't had the issue since. Glad he didn't have surgery! Point being, ,weird things can set off pain in that area.