Today I decided to go run this morning, and it's nothing unusual because I always run in the morning after I wake up. Except last week, I got really sick so I decided to take the week off because I thought running would just make my condition even worse. When I ran this morning it was extremely hard to breathe. I was out of breath five minutes into my run. Usually when I go out to run it's around 60 degrees, but today it was 45. So I'm wondering if the reason I was out of so early breathe was because it was colder or if it was something else, like I haven't ran in a week or if it was because I wasn't eating very healthy the week I was sick (Fast food, very greasy home made food).

I am not a doctor, nor a professional in this area. But, 45 degree weather should not affect your breathing, unless you have COPD or Asthma. I do know that really cold weather does affect breathing with lung diseases. It affected my late wifes' breathing to the point that she could not go outside in less that about 30 degrees weather, without constant pure oxygen.
I think your reaction might be from the illness or sickness. Maybe you had not yet got back to being your normal self. Good luck. If it continues like that with your running, I would see a doctor.

45 is warm where I am right now. I huffed and puffed up a steep hill one day in about 10 degrees, and my lungs hurt horribly. I could just feel those delicate moist tissues trying to FREEZE like a tongue stuck to an iron railing in winter.

I wouldn't worry about your situation. You were sick and out of shape. The lungs have a magical rebound ability, as many smokers find out.