I went through this same thing when my son was 2. He was constantly sick for around 7 months. Everytime He had antibiotics he was ok for the next week but then got sick again. I ended up taking him to a differnet doctor who sent me to an ENT.
The ENT said that he was sick all the time because of his ears....he was always getting ear infections. So he put tubes in his ears and he has hardly been sick since.

If your DD is getting ear infections tell your dr you want to see an ENT it might make all the difference
Good luck!