Two Homeopaths failed on us

I and my family live in Mumbai. My twin daughter and son are 3.5yrs old. They are healthy enough but we tried to take homeopathic route for them at around 2yrs to cope with the regular bouts of viral fever, cough and cold in the city.
We tried a homeopathy doctor in our area. The doctor had a big clinic and fully staffed. They did a case history and gave us some medicine. Few weeks later my children were caught with cough and cold. We visited the doctor and were given some medicine. All the time we observed and felt the doctor never did a proper physical diagnosis. But we thought may be it is the way. But eventually my daughter's chest got too much congested which the doctor was not able to diagnose even after examining the chest. Daughter' condition was not improving and we had to rush to our pediatrician and he could easily diagnose congestion and prescribed an antibiotic. This made us doubtful of the Homeopathic doctor's capabilities and we discontinued there on
Presently, we consulted another Homeopath in our area. We also explained him our previous experience and he counselled us and said everything will be fine. This time again a month ago my children had developed cough and cold. The homeopath had been physicallly examining my children and called us every third day to check the progress. The progress was average even after taking his medicines for 10 days. Meanwhile my daughter developed fever. So we went to the homeopath and he checked her chest and throat and said everything is fine no need to worry, we can continue with paracetamol for fever. However the fever was very high 104c at night. So we got a bit apprehensive and went to our pediatrician. We were shocked when he said that our daughter had bad throat infection. Infact there was pus formation on her throat which he showed to us.
We just could not understand what the homeopath doctor had been observing. How could he have missed an easily visible pus patch in the throat.

We are very confused now, as how to approach homeopathic remedy. The doctors fail so easily. I always felt that just taking extensive history does not help, the doctor should have experience in diagnosing the patient. I felt they always relied on patients identifying the physical cause of trouble.