It's not that hard to justify being able to heal wounds but not illnesses.
After all, there's a fundamental difference between a wound and a disease. One involves extensive damage to your body and the other involves a harmful living pathogen causing harm inside your body.
By that logic, applying healing magic might be able to temporarily cure the symptoms of a cold, but the microbes causing the problem can cause it to come back again immediately. Not to mention, things like fevers are probably more the body itself's natural reaction, so it's possible there won't be any response there either.