My son has always suffered from allergies. But this time he has burnin throat and his chest burning on both sides. Also been coughing. What is it?

Infection or reflux. Kids with allergies can have asthma, but usually a parent can hear a wheeze if you listen carefully. The burning sounds like inflammation, which is usually an infection, especially with the cough. Repeated heartburn can cause burning throat, but generally not a cough. If he is short of breath or has a high fever, get him checked out for bronchitis or pneumonia. Try pain and cough meds.
Allergies/infection. Allergies can cause those symptoms. However, more often, viruses will produce the symptoms you describe. You did not mention a fever but that would point to an infection. Generally treating the symptoms - fluids, steamy showers, honey - will help. If not improving, he should be checked.