Leg burning sensation can result from a number of causes, including damage to nerves in the legs from exposure to extreme heat or cold or to toxic substances. Leg burning sensation might also result from a circulation problem that impairs blood flow to the legs, a leg injury, or intense exercise.
Swollen feet can have several different causes. They are all do to increase in the amount of fluid in your feet and ankles. Since you swelling seems to happen later in the evening, and you have no other symptoms, I would guess that your swelling is due to venous insufficiency. This is when the veins in your legs have trouble getting blood from your feet back up to your heart. It is the most common blood vessel disease.
There are a few other causes of foot swelling: a) Obesity: obesity can cause swollen feet and ankles due to the excess weight going through the feet b) Prolonged Standing: standing or walking for long periods can lead to swollen feet and ankles c) Gender: edema is more common in women due to the hormone progesterone which causes fluid retention e.g. swollen ankles before menstruation