Keep in mind that all sick birds do better when kept in a cage that's 80-85 degrees. I know it can be hard to bring them inside, but trust me, they will do better. Also note that this is not something I made up, it's something that many avian vet books recommend, and it's something I do whenever I have a sick one.
Regarding Corid. A quick search I did on coccidiosis vaccines said you should not use a coccidiostat within the first few weeks of them being vaccinated. This would include medicated feed, Corid, all sulfa drugs, Baycox, etc.