Is this asthma? This medicine course?

Chest Xray showed hyperinflation of lungs but doctor said you might have taken a deep inspiration, and xray looks normal, attached xray. Also attaching pft reports.. Please help me to understand what it is as ent said it early indications of asthma but not developed yet. Medications i am on: AB Phylline 100mg, Alex Syrup, Prustalin(antihistamine) It has reduced my cough almost to zero but i still have phlegm production and post nasal drip mostly. (When i take prustalin it reduces). H/o: - Non smoker - No exposure to chemical fumes - Mother(63) asthmatic - Ige level 440 - esionophils last checked: 10.5% - had frequent tonsil infections in past Please advice. Current symptoms: Cough has subsided greatly but tickling at throat remains, dry cough sometimes, post nasal drip and mucus production in throat which leads me to clear throat multiple times.. So, is the xray and pft normal? And is this asthma? Should I go for inhalers now after this medicine course?