Hi, Thank you for your question. Burning sensation, numbness or tingling sensation in any part of body is considered nerve related in origin. This burning sensation you are having can occur due to impingement, irritation or compression of nerve of leg or spine. Most frequently involved nerve is lateral cutaneous nerve of thigh (which is branch of femoral nerve). This condition is called meralgia paraesthetica which manifests itself as pain, tingling or burning sensation of knee. It may occur due to injury to nerve either due to spinal deformity or along its path to thigh by any ligament or tendon stretch, excessive tight clothing (therefore it is also called "jeans disease"), diabetic neuropathy or damage to nerve after surgery etc. Another nerve which may cause pain in legs is sciatic nerve compression. I would advise a CT scan of spine and thigh, blood sugar levels, and EMG to check out abnormal muscle responses. Hope this helps.
The most common etiology is sciatica.
I would NOT advise a CT scan.
An MRI of the lumbar spine provides better information at less hazard from radiation. The CT, while acceptable, is obsolete for this purpose.
It will probably get worse.
Do a search on "sciatica".
There are special exercises that will relieve the pressure on the nerve.