How can heavy breathing be treated?
Your heavier breathing could be, as you suggested, due to your recent lifestyle changes. But do assess whether the following could be responsible:
Increased levels of pollution
Extreme weather conditions
Changed area/place of exercise (or indoors)
Suggested check-up of upper respiratory ailments
You can also include a longer period of a warm up so as to help you ease into your routine. This will also help you build your aerobic capacity in a steady fashion. And like you said, as you train, you should find a noticeable change.