Have your doc check your iron levels, you may have a deficiency that worsens during your period due to blood loss.
Could be sign of uncontrollable diabetes too
It depends on where they're burning. If it's a sunburn, an aloe gel can help the pain for a while. If it's muscular you probably need a massage and some regular stretching. If you have shin splints, you need to stay off them for a while and ice your shins. Also, look into buying running shoes with good arch support.
Other causes of generalized burning leg pains may be some sort of nerve disorder or a pinched nerve. You may have problems with small blood clots that are clogging up capillaries and causing cell death, which can lead to generalized burning. For these, you should go see your doctor as soon as possible.
Another possibility is that the pain is psychosomatic, although this is remote. If your doctor says that there's nothing wrong with you, or that your pain is idiopathic, I recommend consulting a psychiatrist for an evaluation, just to cover all your bases.
Other causes of generalized burning leg pains may be some sort of nerve disorder or a pinched nerve. You may have problems with small blood clots that are clogging up capillaries and causing cell death, which can lead to generalized burning. For these, you should go see your doctor as soon as possible.
Another possibility is that the pain is psychosomatic, although this is remote. If your doctor says that there's nothing wrong with you, or that your pain is idiopathic, I recommend consulting a psychiatrist for an evaluation, just to cover all your bases.