Could it be bad if you can only breathe through your mouth?

Yes: When you breathe through your mouth you also dry the tissue. This means the saliva, a natural ( and maybe most important) protecting agent for your mouth against cavities and gum disease is removed.

Mouth breathing: Chronic mouth breathing can not only affect your quality of life, but also cause major health problems. It can lead to poor sleep, gum disease, snoring and compromise the immune system. It is a common condition, but often overlooked and ignored.