Law suite against pediatrician? can it happen?

my daughter has barely been able to breath for a long time shes 7 months old. she has had 3 ear infections, and currently has a staph infection. I have taken her to the doctor repeatedly over the staph not getting better but spreading and she couching sneezing runny nose terribly congested and weak state she has been in for a month or more. He just told me it was a cold and that they cant give her anything. and no matter how much i asked we wouldn't run any tests. I took her to another pediatrician today and right away he did the works. She had Bronchitis and the staph isn't being killed by the antibiotics. Can i suite the doctor that wouldn't run the tests? I don't want money but all this is if i had kept believing him could have seriously hurt my daughter. I changed doctors but what else can i do? What are my daughters rights?