Burning sensation that started in my head now spreading to my neck, back chest and arm. What could be no rash. Feels inside my body. Worsening.

Could be nerve pain. See your doctor for a thorough history and physical exam. Best of luck!
Nerve pain. It is difficult to say without examining but the pain you are describing sounds like nerve pain. Nerves can get pinched at the level of the neck giving burning shooting pains in the arms and neck. The chest and back pain may be due to referred pain from a pinched nerve as well or due to inflammation of cartilage. You need to get examined by a doctor to get the correct diagnosis.