For the past few months, when I am on my menstrual cycle, I continue to have a burning sensation the entire time. This is the only time it happens?

Go see an OB/GYN. There are a few causes of burning with your cycle. Most of these are easily managed with medications. Unfortunately, an exam would have to be done to accurately diagnose which it is. A gynecologist should be able to do the work up you need.
Possible yeast. Many women have a change in the yeast levels in the vagina around the time of their periods. This happens because our hormone levels drop and this allows more yeast to grow. You may need to use a medication for yeast.