Running will certainly feel challenging at first and you will be slightly out of breath when you start. That should eventually subside. It's helpful to use the "talk test." If you can hold a conversation while you're running, you're at a good pace. Once or twice a week, however, go for a shorter run at a faster speed so that talking is more difficult. This will help increase your fitness level and cardiovascular strength.
Your legs will be sore in the beginning, but if you keep up the routine, soreness will subside relatively quickly. If you feel acute pain anywhere, stop running for a few days and let your legs recover, to prevent injuries. Be aware of the difference between being tired and being injured, and make sure you're not encouraging overuse injuries.