I am 14 weeks and have also been experiencing shortness of breath. It's totally normal.
Shortness of breath is common. Early on your lungs expand to help support baby and this can cause a feeling of shortness of breath and later on baby gets big enough they push organs up, pushing them into your lungs makeing you have shortness of breath.
Sounds like you may have low iron, which is common in pregnancy. Call your doc and you can get a blood test and put on supplemental iron if that's the case.