Why is my 16 month old constantly sick?

My daughter is 16 months old. At about 6 months she began to get a rash on her arms and legs and cheeks only. The doctor said it was eczema and has since given her 3 different "lotions" that were supposed to help, but nothing helped. She still has it today. Around the same time, she got really sick; runny stuffy nose, cough.. we had to call an ambulance to the house because she stopped breathing at one point. 2 doctors and an emergency room pediatrician told us she was fine, just a cold!! So I took her to a new doc who said she has a sinus infection and prescribed antibiotics that made her better right away. I was so relieved. (Rash never went away still).So since that incident, she seems to be sick constantly. It seems like her nose is never clean of the crusted dark snot, shes always coughing, always runny nose, yellow diarreah, now there is a different rash on her chest, stomach and face. Sometimes she has a low fever. I am told by her doctor that he cannot find any infection, that shes fine. How can she be fine? I am so frustrated, shes also recently had pink eye twice!! I was blessed with very healthy older children, who never got sick barely ever... now I dont know what to do with this one. Does anyone know of anything that could be overlooked?? Other than being congested and annoyed with all of her symptoms, she typically acts fine, she has energy, shes playful, she has a fairly good appetite.. I dont know what to do anymore.