Hi
Thanks for writing to the forum!
Birth control pills can cause clots in pulmonary vein and affect breathing. They can also increase your weight and thus make breathing more difficult. Please consult your PCP as it is not normal to have breathing problems.
It is difficult to comment beyond this at this stage. Please let me know if there is any thing else and do keep me posted. Take care!
No It shouldn't affect your breathing, Go see your doctor if you can't breath. It may be asthma or pneumonia!