Is it normal to run out of breathe when I exercise?

Yes. When you exercise, your muscles need more oxygen to work, which is why your heart beats faster and your breathing rate increases.This is normal. The better in shape you are, the longer it will take before you get out of breath. There are, however, some medical conditions that can cause this, such as asthma or heart issues or anemia. Best to get an exam to assess, especially if your symptom is new.
No. You should see your pcp to make sure you don't have exercise induced asthma, a previously unknown heart or lung problem and to discuss your symptoms.