Bakugo has the Hanahaki disease. Its a disease in which he coughs up flower petals that grow in his lung beacuse he suffers from a one-sided love. If not treated, the disease is fatal. It can be cured when Bakugos love interest returns his feelings for the rest of their lifes. He doesnt want anyone to discover his disease. It got worse in the last days.

You noticed Bakugo was coughing a lot during class. He stands up, asking to go to the nurses office. But instead he goes to his dorm room.