There are many types of antibiotics.
IF a certain antibiotic does not work... THEN, the Doctor should be trying ANOTHER family, of antibiotics.
I am surprised, the Doc did not do any tests on him.
Nor see if it is Pneumonia or Bronchitis, etc.
Mucus/congestion, can be from 2 sources:
lungs, or
Sinus, post-nasal dripping.
And, it can occur both at the same time.
Post-nasal dripping, can also infect the lungs. And because a young child cannot "spit" out mucus accumulation.
I had a cold once. Then got Pneumonia. My Doc said it was an infection from my continual post-nasal dripping. For example.
Secondary infections can also occur.
Is he having labored breathing?
Did they check his oxygen levels?
Typically, a course of antibiotics does have to be taken... to see if it is working or not.
And take it for the full course. Do not stop midstream.
TELL your Doc, to try another family of antibiotics.
If the current type, is not working.
OR, take him to the ER.... and see what the ER Doctors, say.
BECAUSE, this would be a 2nd, opinion on your son's condition.
Keep in mind, that nebulizers or inhalers, do NOT stop the mucus or congestion, nor does it "cure" the illness. What it does is open up the lungs airways.... so that breathing can be improved.
I have asthma... and this is what it does. Because with Asthma... the airways are constricted or inflamed... hence, a person cannot breathe fully and it impedes the intake of oxygen in the system.
I would take him to the ER.
Your son is young.
Continued lung illnesses, can weaken the lungs.
I personally would not send him to daycare. He is sick. AND I wouldn't want to infect, other kids with an illness.
Contrary to what your Pediatrician, said.