Hopefully a cough or a wheeze signifies a common cold, but there is a correlation between allergies and asthma. If your child's allergic symptoms have progressed to coughing or wheezing, it is definitely high time to talk to your pediatrician.
In addition to looking for medical symptoms that differentiate allergies from illnesses, your pediatrician will probably order a patch test. This consists of sticking a grid with small amounts of different allergens, such as plant pollens, onto your child's skin. After a period of time, the patch is removed. Red spots on the skin indicate an allergy to the substance in that quadrant of the patch grid.
Allergies and asthma are chronic conditions that require treatment and control, so be sure to share your suspicions with your pediatrician. Your observations as a parent provide the best help to your child's doctor as she selects the groups of potential allergens to test, and helps you decide on the best course of treatment.