Flight Instructor reported a CO level warning came on during cruise and the instructor initiated an immediate return to departure airport. Instructor stated the student had physiological reactions requiring medical attention.

Narrative

On our training flight we went out north to a practice area X. We were at about 5;000 feet MSL heading North when a CO level warning came on. My student quickly canceled the message but I was able to catch a quick glimpse of the message. At this point I decided to turn back to ZZZ and conclude the lesson. I had opened the storm window and shut off the heat/defrost. I took flight controls and started a descent down to 2;500. The descent was steep but nothing out of the usual (taking into consideration the rate of descent during a simulated emergency descent). However; on this descent my student bent over and grabbed his eye and started complaining of severe pain behind his eye. I contacted approach an informed them about the high CO level warning and that my student was in considerable pain. I requested priority for landing and a straight in approach for the RNAV XXR. We leveled off at 2;800 and proceeded towards the Initial Approach fix. During this time period I was in constant communication with my student. He remained responsive but continued to experience sever pain. I told him I would keep talking for the remainder of the approach discussing items related to the approach. I told him to listen to me to make sure I was making sense when I was talking just in case I started succumbing to the 'CO' without knowing I was. During the flight inbound we both noticed a chemical smell in the cockpit. We landed the aircraft and were escorted by the firetruck and ambulance. I asked to taxi on XYL to taxiway X onto ramp. Once we were there I shutdown and had my student go into the ambulance to get checked over. They said he should go to the doctor the following day.I believe there was a leak from the exhaust into the cabin. I did have the heat/defrost on which utilizes the heat from the exhaust. I assume there might have been a crack in the exhaust system that resulted in CO coming into the cabin.Our aircraft are usually kept to a very high maintenance standard so I would not recommend anything on their part. However; I would recommend a possible redesign of the heating system/exhaust systems from the manufacturers that would make it harder for CO to get into the cabin.