It sounds like what you have is muscular. Some cases of myositis (polymyositis or dermatomyositis) do have pain, swelling and a burning sensation. I have PM and had it in all of my muscles.
However, the pattern of weakness is usually distinct...symmetrical and is characterized by difficulty getting out of chairs, going up stairs, and raising arms over your head. EMG is used by some docs to diagnose it but not all. Cpk is not reliable...you can have an active disease state with a low or normal number and yours were not high. Lupus can cause similar problems but is usually not as distinct.
The only conclusive way to diagnose myositis diseases is with a muscle biopsy but your doctor should be fairly certain based on other symptoms and labs before doing that. There are a number of other neuromuscular diseases that could produce symptoms like yours.
If your current doctor is not being aggressive get a second opinion but make sure the rheumy or neuro is experienced with AI diseases.
MCTD (lupus, scleroderma, polymyositis). Diagnosed 2005. Kidney, liver, GI tract, dysphagia, raynauds, Barretts esophagus, quadriplegic in 2005. Recovered and now active in skiing, tai, chi, hiking, golf. Meds: prednisone 2.5mg, imuran 25mg, amlodipine, benazapril, omeprazole, potassium, folic acid, vitamins, maxide and various supplements and vitamins.
Remain optimistic and you can overcome the odds.