Hi dear, Sleep apnea
doesn't go away with nasal sprays, humidifiers or antibiotics, children with sleep apnea might get cold
more than others, perhaps that's why doctors suggested giving her puffer or nasal spray just to reduce cold symptoms.
Sleep apnea is more of an underlying condition by which muscles at the back of the throat tend to relax making it difficult for the air to pass in and out of the lungs, children with this condition have loud snoring
while asleep, sometimes breathing is disturbed (or you can hear like a chocking sound while sleeping).
The first line of treatment sleep apnea is surgery by removing tonsils and adenoids
to ease airway passage.
The best thing i would suggest to do now, is to go to an ENT specialist
to evaluate your daughters situation and severity of her condition, the ENT will then decide if she needs surgery or not according to her situation.
Since she is just 4 years old and from the way i read your question i believe her situation is mild and perhaps she doesn't need surgery now.
Wish you and your daughter all the best.