Is it common to have trouble breathing after breast augmentation?

The swelling and tightness is normal. Trouble breathing could also be a result to your breast implants, but you need to discuss this with your plastic surgeon now. Best wishes, Dr. ALDO 

but if you've made it through the night, its most likely from the pressure and discomfort of your implants on your chest and this will get better.  In this scenario, you feel challenged to take a breath but you're not really short of breath.  In the other scenario, it involves your surgeon to have punctured your lung and this creates a pneumothorax and acute shortness of breath where you simply cannot breath... this is an emergency.