The burning is typical of neruopathic [nerve ] pain.
When there are disc problems in the lower spine this is never isolated and there are at least minor problems elsewhere and this is what is one possibility for your pain.
In addition, postural abnormalities because of the lower spine problems can cause constant stress on the upper musculature in the deep paraspinals and cause the same type of pain.
This can be remedied with the assistance of a physical medicine and rehabilitation MD this is a type of specialist and you do not need a referral, but this doc will do a whole body integration analysis and correct this problem with physical therapy
...the right type which is often not done....appropriate electronic or traction therapies etc.
This should be your next step
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