How Long Should I Give The Medication For Nasal Infection?

hello, My daughter is 2 years and 9 months. This year she has been suggested to many nasal infections which later revealed that her adenoids got bigger. the pediatrician recommended Nasonex spray every morning and Aerius syrup for allergies every night. I always seem to notice that she breathes through her mouth (i can hear her breathing when she is next to me), she drools (sometimes during the day but mostly at night) and her cough is still present. Add to that, I see her rubbing her eyes and she has puffy eyes especially in the morning (which proves that she does have allergies). How long should we undergo the treatment to feel the difference? Should we seek an ENT specialist for further investigations or just give it time since no complications are there? Thank God she is growing as she should, she eats well and plays also but some phoenics when she speaks are not very clear, and sometimes she stops in the middle of the word to breathe