Are burning hands a symptom of diabetes?

Possible neuropathy. Neuropathy can happen as a result of trauma, or nerve damage due to the consumption of alcohol or certain medications. Symptoms can range from a numbness and tingling sensation, possibly a burning sensation, to an uncomfortable painful sensation of the extremities. Get evaluated by a professional to determine the exact cause in order to get the appropriate treatment.
Not early. Generally not until very very late after many years. If you're concerned, see your doctor.