When you go running you need to wear the best sports bra, one that will prevent skin chaffing.
You should also wear a proper t-shirt.Your classic cotten shirt is not going to wick away sweat. This makes them get damp and stay damp. Besides being uncomfortable, they also can cause skin irritation.
The best maker of running shirts and sports bras for jogging is Under Armour. They are made of a material that wicks away sweat and won't cause skin irritation.
It's important to pick the right sports bra because it can prevent breast rash.