While I agree with Stormcrow's long answer, as a fellow "shellfish" allergic person, I'd like to help you simplify this a bit.
You do have to know a bit more about just what you are allergic to. For me, when I was told I was allergic to "shellfish," the allergist meant crustaceans (shrimp, crab, lobster). I can and do eat mollusks (clams, scallops, oysters). Though, like Stormcrow implied, I later found I could eat our local California spiny lobsters no problem if freshly caught, which we do on our sailing trips, so it the diagnosis isn't that cut and dried. Haven't bothered to find an allergist to help me nail down the specific allergen because it doesn't bother me to avoid those foods. I do have to be careful of farmed fish such as trout that have been fed shrimp shells to turn their flesh pink, as I get a mild reaction from that.
Oysters are a mollusk. Mollusk shells are not "alive" in the way, say, a turtle's or a shrimp's shell is, even when the animal is alive. The shell is mostly calcium carbonate, a non-living mineral laid down by the animal's living mantle. A living oyster's shell would be about 98% calcium carbonate and about 2% protein (the only potential allergen). By the time it is dried and processed for chickens, I don't know what the percentage would be or even if any protein would survive at all. Calcium carbonate derived from shells is often included in vitamins and foods, and the FDA does not require that it be labeled as "derived from shellfish" and hence a potential allergen. But the time it has gone through your chicken's digestive system, it would be even less likely to cause problems than when consumed directly.
In short, judging by the FDA I think you are good, unless you are violently allergic to the mere whiff of oysters.