Is asthma completely curable? Curable?

I have asthma , sinuses and my father has also asthma problem .I am under treatment since  last 3 years .Doctor adviced me to take budamate 400 ,1 nasal spray and montair 10 .I was having this medicine last 2 years but it is not curing at all.. recently I visited cmc vellore ,the doctor adviced me to take budecort 200,fexinase ,lukotas for 6 months .frequently I got fever and cold easily .. recently I am facing chest pain and during  this pain I am feeling heavy  breathlessness . Actually the problem is increasing day by day ..I avoid cold things ..but the problems are mainly causing at the time of weather changes .. recently I got influenza ..right now I am feeling well ..but these cold problem coming frequently...is asthma totally curable ??