Oatmeal is high fiber and chickens can't digest the fiber well. So it's not good for sick birds, but good for dieting birds. I wouldn't recommend giving a random antibiotic right away without knowing what disease you're treating. You could be treating for the wrong thing and a pathogen could quickly become resistant that way.
When my birds are sick, I always give them fresh greens. Lawn clippings for sure and definitely chick weed if it's growing. If I don't know what they have, I give them electrolytes and Poultry Cell to help keep their nutrition up to par. Apple Cider Vinegar, yogurt, Motrin (human med), and Hypericum are all great as a part of supportive therapy. I have more stuff listed on my webpage (linked below Moody's Bantams) Poultry Health > Supportive therapy. Cinnamon and cayenne pepper are good for respiratory problems, and dairy, garlic, and leafy greens are good for digestive upset. But the biggest thing you can give a bird... warmth and a secure environment.