How long has this been going on? You may have some type of virus or something. If you are having trouble breathing, you should call your doctor and try to get in soon or go to Urgent Care. In the mean time, you could take some decongestants and then take a hot shower. The steam can help clear congestion, at least temporarily and make it easier to breathe.
As for YAZ, the shortness of breath could be a sign of a blood clot in your lung. Did they give you a chest CT? If the symptoms don't go away, you should go to your regular doctor and ask for a Chest CT to check for blood clots. They can give you blood thinners to dissolve the clot, if there is one.
However, it could also be something else, so don't let the doctors dismiss your symptoms if they don't find a clot.
Good luck.