Thanks for posting your query.
Dengue fever can damage your lymphatic or circulatory system but it usually dose not present with burning feet and hand. Burning sensation can be caused by irritation of nerves by toxins produced in our body, diabetes
and kidney disease.
You should also rule out Vitamin B12 deficiency
by measuring blood levels.
Take healthy diet with low unsaturated fat
and avoid alcoholism. Exercise regularly and drink enough water.
Contact your doctor to rule out disease that can cause burning sensation.
Hope it helps,