Lately when I've been running I start to have trouble breathing and start wheezing probably because I am sick?

Asthma. Exercise induced asthma affects people who don’t have other asthma symptoms. They are more sensitive to temperature and humidity of the air. Cold dry air inhaled through the mouth reacts with warm moist air in the lungs triggering an attack. Breathing through the nose warms & humidifies air which helps. Its hard to breathe through your nose when exercising but a face mask/scarf may help.
Possibly. There are so many potential problems I would see my primary care doc to a physical and rule out any potential problems.