I'm not sure if your second paragraph is aimed at mainstream medicine, or "alternative" medicine. Mainstream medicine does not claim to have a cure for a cold. Mainstream medicine masks the symptoms so that people are less miserable while the cold runs its natural course.
What's curious with your list is that one is a disease ("cold"; the rhinovirus) while the others are symptoms ("cough, mild pain, sore throat"), and the other is an entire class ("psychological problems"). It's hard to respond to what you said because you called them all "illnesses".
What's curious with your list is that one is a disease ("cold"; the rhinovirus) while the others are symptoms ("cough, mild pain, sore throat"), and the other is an entire class ("psychological problems"). It's hard to respond to what you said because you called them all "illnesses".