^^^
That is incorrect. Lots of people have stomach pain from T4s/opiates in general -- it is rarely indicative of an allergy. Opiate allergies tend to be much more serious (respiratory failure/coma/death) and many people who are allergic to one opiate are allergic to all other opiates as well.
Try eating some food when you take your T4s -- it's not good to take them on an empty stomach if your stomach is sensitive. If this doesn't help at all, tell your doctor and he will help you find another painkiller. Explain that your stomach is quite sensitive.
Darvocet is weaker than codeine but by no means "placebo". Some people find that darvocet works quite well for them. Give it a go, you might be one of these lucky people. If it doesn't work, call your doctor and tell him so.