I'm a teen. How will having corns mess up my health later in life?

Foot discomfort. They won't "mess up your life" but they can cause foot discomfort depending on their size and position. They can certainly make wearing certain types of shoes uncomfortable. Diabetics, however, should have corns and callouses removed or trimmed to prevent further problems.
It may not. Depending on the cause of the corns you may not have any problem later in life. But if you have deformities of the toes, the toe position may continue to worsen and create foot pain later in life.