Abuterol Syrup for Toddler

My son had pneumonia at 14 months old. He had to take one medicine with a nebulizer (breathe the medicine as a mist) and other medications as well. Albuterol is a bronchodilator. The Dr would not prescribe it unless he thought your daughter was having trouble breathing. If the excess saliva gets into her lungs, she can have a secondary bacterial infection and end up with pneumonia too.
"Asthma is the most common serious chronic childhood disease, and it's the third most frequent cause of hospitalization in children under 15 years of age. Asthma affects 6.5 million children in the United States today. Fifty to 80 percent of children with asthma develop symptoms before they're 5 years old."
She's not too young to have asthma. Take her to a pediatric allergist for a second opinion, but you're asking for trouble if she seizes up and can't breathe and you are not prepared to help her.

I gave my daughter chamomile tea at the first hint of a cold, cough, tummy ache or pain. It works wonders to calm and ease their symptoms.

I agree with you. I certainly wouldn't jump to conclusions and put her on Abuterol! If the coughing continues, explore other possible causes for the coughing. Perhaps removing all chemicals from the home could be helpful. Check out Kids Safe Chemicals Act.

Take her to someone who specializes in asthma - an allergist, maybe? I understand your concern about not medicating her, but if it IS asthma, then she needs help. Asthma is uncomfortable to say the least and dangerous at most. I know you are hoping it is something else, but if it isn't, then you aren't doing her any favors by not treating it.