The symptoms aren't caused by the same disease over and over. The symptoms are what your body does to fight the virus or bacteria. The cough and sneeze and sniffles are all intended to help your body expel the invader, the fever is an attempt to bake it to death or slow it's reproductive cycle so it can be fought.

Most of the diseases that affect the respiratory system will have very similar symptoms despite being different diseases.

That being said, the rhinovirus goes around, but much like how there's a new COVID Variant every few months, there's a new rhinovirus every few months. You won't catch Rhinovirus A if you e already had it but it's been a very successful virus and has a large family of variations and you might catch any that you haven't already had.