I've never heard of it being weird to dream about your teachers. To your dream self, any waking experience can be used in the dream. Clearly this teacher is a caring person and that has probably touched you. It's not surprising she appears in your dreams.

In the dream, when the teacher remarked that most people would have gone home if they had such a cough, was it more a caring remark (like noticing your suffering and/or admiring your stamina) or was it a more critical remark (like saying you "should" have gone home)?