A lot of us understand exactly what you are feeling and going through, it is truly on of the most horrible experiences there is! A few comments for ya though...
Everyone that has told you that by taking the codeine you are extending the w/drawal is correct. If you really can't manage the cold turkey kick, you may be better off tapering your codeine over a few weeks rather than doing it CT.
One thing that helps me is having gone through this many, many times and coming off much stronger opiates at higher doses is understanding what is going on and how long it will last. Typically, and this would be true for codeine, from 24-48 hours is the absolute worst physically. You can get through this with benzos, lope or any of the other recommended drugs, but either way, it's going to suck, a lot!
Once you pass the 48 hour mark, without ANY opiates, you will gradually start to feel physically better. After the 24 hours of hell, any little bit helps! With such a short duration or your use and the drug you used, the physical should be over around day 3. As mentioned, the mental-shitty feeling takes a bit longer to go.
Everytime you take that nighttime dose, you are almost starting the clock over- so you're turning a 3 day hell into however many days you've been at this. If a taper isn't an option, look into a bupe or other detox- you can detox very quickly, especially from codeine.
Also keep in mind, the farther you go with this (using more and stronger opiates), the worse the w/drawal is. I'm sure it feels like the worst thing you've been through, but trust me it can get much, much more painful and worse! Good luck!