How do you look after a pet seagull chick?

Your best option is to notify a rescue or wildlife organization about the seagull and otherwise leave the poor bird alone. Part of being a wild animal is that when you get injured, you either survive or die - that is the rule of nature. Humans interfere sometimes, particularly with endangered species or when the damage is obviously caused by humans (such as the Gulf of Mexico oil spill). Otherwise, you risk being hurt yourself and hurting or killing the seagull by trying to take care of it yourself.