What are the risks of drinking cough medicine every day?

Depends. It depends on which cough medicine. If it is a prescription cough medicine... It may have Codeine and if you are using it daily... Then addiction could be a problem. I would try to figure out what is causing the cough: asthma, acid reflux, allergies, sinususitis, rhinitis (drainage from the nose).
Cough medicine. Depends if the cough medicine has Codeine in it. You face the risk of addiction. There should be no need for such regular use or abuse. The cough itself may need to be evaluated.