I believe this is your trachea, if you are feeling both sides of your throat at the same time you may be unconsciously applying more pressure or force to one side or the other giving you the impression that one side is larger than the other. I seriously doubt you have cancer, I've been smoking for about 7 years now, a pack a day for probably past 3-5 years.
Other possibilities are perhaps inflammation of the throat do to allergies, respiratory irritants and things of that nature. Perhaps you are experiencing a "knot" of muscle tissue that surrounds the throat. If you don't have any blood in saliva, no pain or anything indicative of cancer i think you can relax a bit. That being said, everyone's bodies are different and even though its unlikely you have cancer might want to consult a physician.
If you have been sick recently or experience a runny nose or things like that its possible there is a mass of mucus that is obstructing your throat. I would look into that possibility if you find yourself in the habit of sniffling or "snorting" substances.
All things considered the trachea is quite flexible and i'm guessing you're just pushing one side harder than the other.