When I breath in or out I taste blood in my mouth but there isn't any, and when I cough I feel like I'm coughing up blood but I'm not. Why is that?

Dental or medical? Your problem might be as simple as a dental problem, i.e. Bleeding gums or a periodontal problem. Start there, and see your dentist to examine your mouth. If all looks ok, make an appt with your primary care physician for an full examination.