Most women can resume full activities, including running and push ups, bu 6 weeks. I would select a sports bra that holds and compresses the breasts well and minimizes movement with exercising.
Running after a breast augmentation
Running and other high impact exercises are the last things that I would add in after a breast augmentation. I recommended waiting about 6 weeks for these activities due to the bouncing and stress on your breasts even in a good bra. I recommended wearing a bra the stabilizes your breasts and gives some compression so that there is as little movement as possible. Chest exercises can be added back in once healed and once the muscle spasm or irritation has settled (for those implants placed under the muscle). This can be anywhere from 1-3 months after surgery.