Is it an internal burning? Like deep inside the breast? Or is it the skin or nipple? Is there any discharge? It could be several things. I am no expert, but do know that women experience pain from hormone fluctuations. It is also possible that you have some sort of infection. Possibly bacterial. That is possible even without discharge. I am not certain if breast cancer would cause a burning sensation, but I imagine it could be possible. I know that's not what you want to hear, but it is also highly possible that you just have an infection that could be cleared up with antibiotics.