Laryngoscopy is a procedure done by specialist till your neck level or upper respiratory level to view the larynx and surrounding area for problems like voice change,
hoarseness of voice,
dyspnea, irritative cough etc. It can not affect back spine in a practical way.
There is possibility that his spine was extremely weak due to
osteoporosis and due to some improper posture while doing the procedure spine came under pressure and he started having the problem.
Burning sensation and pain in back shows damage to either
soft tissue near the spine or damage to
spinal nerve or disc at that level. How ever the conformation can be done by MRI of affected spinal level.
Based in result here you have to take opinion from spinal surgeon or orthopedic doctor on further treatment planning. Boost the patient with calcium and vitamin D as directed by doctor. In severely damage spine here doctor may ask for surgical correction also. In that case you can also take secondary opinion and go ahead with needed treatment. After this consult a physiotherapist for
rehabilitation part and also take suggestion in posrtuee as well spinal exercises which will help the patient further to improve strength and stamina of spine.
You can also use hot pack at home for some more relief and soothing effect on soft tissues.
Take care.