I have been coughing, a sore throat, and the inside of my nose has a burning sensation. Any idea why my nose burns inside? It also is hard to breathe

Cold or allergy. Your symptoms can either be related to a viral infection or to nasal allergies, both can irritate your nasal passages and make your nose sensitive. Use a saline nasal spray to soothe it, it should help you until you get your symptoms checked with your doctor.