Is it possible to have multiple pinched nerves (ie. thor and lumb simultaneously)? burning muscle/ache/fatigue in shoulder/arm and low back/bum/thigh.

Possible : But the described symptoms of fatigue, burning, and aching muscles involving the "bum"//thigh and shoulder/arm (proximal muscles) are most likely due to something else. In a 29 year old female, this should initially be evaluated by an exam with your medical doctor along with blood tests +/- spinal x-rays.

Yes and no: You can have multiple location pinched nerves yes. None of the symptoms you describe are typical for a pinched nerve. See your primary doc for a workup, they may consult neurology on this.