My chest and throat burn when I take a deep breath. And sometimes it makes me cough as well?

Throat chest burn. The reason for this something causing inflammation on those areas. The two most common reasons would be an infection or acid reflux.
See a doctor. You can start with a pcp and they may wish to refer you to a pulmonary (lung) specialist. Need more history and an exam before could begin to speculate about what may be going on.