I f your peak flow is 600 it is unlikely you have asthma.
however wheezing is either asthma or some other airway obstruction
highly likely is that you have chronic sinusitis from your cold and have a post nasal drip where mucus is dripping into your lungs causing irritation
Ask for an ENT referral - this needs to be excluded if your symptoms have been going on so long. Asthma doesnt just happen like this
Best wishes