I can say that with over 99% confidence, as a real allergy to codeine is about as common as a customer that is aware they have insurance and has the proper card available to help me file a claim. Or an insurance reject message that actually has something to do with why a claim is being rejected ("missing/invalid alt bin variable code est. error" doesn't do a lot to point me in the right direction insurance industry), but I digress. You're not allergic to codeine.
I can hear the howls of protest now. I don't know why, but people seem to be proud of their allergies. It makes them feel special, like they are getting some sore of extra care or attention by making their doctor write for Toradol ( a med far more nasty than any offspring of Narcos) instead of a short course of Vicodin. Ask most people who swear on their mothers grave they are allergic to codeine and anything even distantly related what it does to them however, and the most common answer you'll get is it makes their tummy hurt. Well eating Spam (the so-called food, not the e-mail trying to cut into my Viagra sales) makes my tummy hurt, but I'm not allergic to Spam, my tummy just doesn't like it, and your tummy just doesn't like codeine. Chances are we could coax your tummy into tolerating it by having you take it with food and/or an antacid, but most of the time I know not to even bother. Given a choice between feeling special and enduring extra pain, most people will take the pain.