Hi,my Daughter Is 3.5 Years And We Have Recently Shifted

Hi,my daughter is 3.5 years and we have recently shifted bto this new posting place..Chandigarh from Secunderabad.. As soon as the winters arrived in Nov '15.. My daughter caught this cough n cold.... Doc told us this is allergic and will keep occurring till she turns 5! Now recently I noticed that she coughs a lot especially after in deep sleep.. Again had to c the doc...and this time he has told us to nebuliser with2.5ml Asthalin respules thrice a day for 3-5 days and to be reviewed after that.he also told me that if no respite he will start budecort after day 5th.. Is she going to develop Asthma.. I M really so worried. Her father also has some allergy to unknown allergen... And so do her paternal grandmother.. Pls guide me though the clouds of doubts!! How long i T will continue