I had a root canal last summer. Now that tooth is causing pain. It hurts to breathe air in through my mouth, eat from that side, or drink. I thought since the roots were gone, it could not hurt. What could be wrong?

Root canal. Even tho there is no nerve in the tooth depending on how many canals were found when the root canal was done there can still be a extra canal, fracture, decay under the crown, tooth got re-infected or a different tooth in the same area that can all be possible reasons why you my still be having pain.
You. You need to return to your dentist and have and x-ray and and examination performed on the tooth. The roots of your teeth are still there - during the root canal - the dentist cleaned the soft tissue out of the roots of the teeth with slender files and sterilized the roots with medications. During this follow up examination - the dentist will check to make sure that the tooth has been properly restored, that re-infection has not occurred, and that there are no hairline fractures on the tooth, and that your bite is correct. After gathering and assessing all of this information - the dentist should be able to develop a plan that will get you out of pain.
Another tooth? I agree with the other answer. But it may also be another tooth... Have your dentist check the other teeth also.
One or more teeth. First, rct removes the nerves and tissues within the canal (s) of the teeth and not the roots themselves. If well done, you cannot have pain to cold, heat, etc. You can have spontaneous pain or pain to pressure if something is still wrong with that tooth, and that can be one of many causes. You may have pain as a result of that tooth, another tooth or several teeth. See your dentist to evaluate.