Is it bad eating ice cream when i have the cough?

No: There's no reason to avoid a food you like just because you're ill. However, it's a good idea not to overindulge in foods that aren't high in nutrition (albeit ice cream is a good source of calcium). As long as you're getting plenty of fiber, fluids, fruits ; veggies, nuts, olive oil along w/healthy protein, you should be fine. Mediterranean diet has most evidence demonstrating outcome benefit.