K.O.
I Would suggest seeing a different Dr. and getting a second look. When my daughter was 2 1/2 she had a constant cough, and runny nose from Aug-Mar. At first I thought she just kept getting colds but it turns out she has asthma. She doesn't wheeze like most people think asmatics do. She just coughs a lot. They Dr. gave her inhalers to use when things are bad and occasionally she use a nebulizer. She's now 4 and does much better now. I hope this helps.