First of all, most parents aren't familiar with the course a disease takes, so they can mistake what appears to be "getting better" for actually getting worse, much, much worse.
Second, "alternative medicines" that have stood the test of time--that work--aren't called alternative medicine; they're called medicine. Props to Tim Minchin.
Here's why you don't want to "treat" your child with holistic medicines to the exclusion of proper care from a licensed healthcare provider: In a heartbreaking case, Tamara Lovett, a Canadian mom from Calgary, Alberta "treated" her seven-year- old son, Ryan, who was sick with not just one, but several treatable illnesses, with "holistic medicines." He died. Had she taken him promptly to a medical doctor, he would be alive today. She stood trial and was found guilty of "failing to provide the necessaries of life, causing death." I don't want that to happen to you. More important, I don't want your child to die unnecessarily.
Now there is reason to be concerned about the over-use of antibiotics, and you should talk to a licensed healthcare provider if you are wondering about that. There's also a very helpful book available to help you talk intelligently with that doctor. Breaking the Antibiotic Habit: A Parent's Guide to Coughs, Colds, Ear Infections, and Sore Throats by Paul A. Offit, MD. Caution: reading this book, even repeatedly, does not make you a licensed healthcare provider, and you need to take your child to a real one. Use this book to help you have intelligent conversations with healthcare providers.