Is an allergy causing my dry tickly cough?

I have had a dry tickly cough for over 3 years and have had a chest Xray which is clear. My GP says I have asthma but I do not wheeze or get out of breath and cough when I take inhalers. I have an intermittent tickle in my throat which causes me to cough. We have excluded reflex and nasal drip. I find that avoidance of cow dairy helps a lot and I will cough if I drink cows milk, butter or milk chocolate. I use goats milk instead which. My GP does not accept that this has any affect. Strong smells, smoke and dust set me off too. How can I find out if I have an allergy of some kind causig this cough?