My daughter had these same symptoms and was prone to getting sick when she was small and main symptom was cough and running nose Frequent colds.Many step throat issues over a year she had it. I got her tested for asthma and was positive and now she is on meds and hasnt been sick like this anymore. I Took her to a pediatric Pulmonologist . She takes Flovent in morning and evening and albuteral when needed which has been almost never once last year. She is doing so much better. Also they removed her tonsils and adenoids She had scare tissue built up in tonsils from the many bouts of strep throat and coughing.
If she is in daycare, this isn't really unusual. Also, is she around anyone who smokes? That can weaken a child's immune system. Hope she feels better soon.
anti biotics are not working now as they used to I am afraid ..and it sounds like she has had enough ..I would check out allergies ..and try her on an anti histimine ..ask the Doctor what kind ..good luck let us know how she is doing .