I caught a cold from my preschooler and now have had 2 months of postnasal drip and cough and mild wheezing is this allergy or asthma ?

Allergy and asthma: It seems like your symptoms were triggered by a viral illness. Remember 'viral illness' does not last two mnths. Well! allergy ( nasal drip), asthma ( wheezing) and eczema are related and can co-exist in same patient and families. Consult your doctor for management.

Possible sinusitis: A sinus infection can complicate the common cold and present with chronic post nasal drip, cough and fatigue. It can also exacerbate asthma leading to wheezing. Allergies can develop at any time, but chances are virus first, complicated by sinus infection now triggering lower respiratory symptoms. Wheezing symptoms would indicated a need to see physician.

Postnasal Drip: Every day, glands in the linings of your nose make about a quart of mucus each day. The excess can come out of the nostrils -- that’s a runny nose. When the mucus runs down the back of your nose to your throat, it's called postnasal drip. http://www.webmd.com/allergies/postnasal-drip