When you first notice it, you might not feel you are short of breath or experiencing breathing difficulties as much as you simply notice your breathing more. This feeling can start as early as the first trimester of your pregnancy, though most women report that they start noticing changes in breathing patterns at some point during the second trimester. Later on, breathing will become can become more than just something you are more aware of, and start becoming a real problem for many pregnant women, especially at night. Slight shortness of breath during pregnancy is completely normal.
Paying attention to your posture, going for regular walks, and exercises (prenatal yoga is a good one) can help with it. Once your baby drops into your pelvis during the end of the third trimester, your internal organs including your lungs will have more space again. When that happens, you will probably no longer be short of breath. If you have preexisting lung problems or asthma, this can get worse during pregnancy. In that case, it is best to discuss your condition with your doctor as early on in pregnancy as you can, so that you can look at possible solutions.