What causes burning in inner ankles ?

Nerve irritation. If it is both ankles then i would be suspicious for nerve irritation in the low back as the cause. If it is just one side then it could be the back or a local nerve injury (saphenous nerve). This also could be early nerve problems due to diabetes affecting one or both legs.
Nerve. Burning is typically a "nerve" symptom. It means that a nerve is pinched or otherwise compromised. In certain conditions it may also represent inflammation in the posterior tibialis tendon, arthritis in the ankle or talo-navicular joints. Your orhopaedic surgeon can help you find the diagnosis and guide you with appropriate treatment.