Burning sensation in right arch of the foot?

A few things. It could be due to plantar fasciitis, an injury, overuse, worn out shoes, tarsal tunnel syndrome (think carpal tunnel but at the ankle level instead of wrist), arthritis, peripheral neuropathy due to radiculopathy (spinal nerve issues) or medical reasons (such as diabetes, thyroid or circulatory issues). See a doctor to have all this sorted out for you.
Nerve damage. Several possibilities ligament abnormality/fasciitis neuropathy/nerve damage radiation from disc problem consult podiatrist.