The thing is with running/jogging is that you have to build your stamina. Today, after 4 months, I achieved a 30 minute sustained jog for the first time. The first time I jogged in Jan, 3 minutes killed me! and after two weeks of jogging for 3 minutes, that was easier and I started doing 5 minutes.
You have to build yourself up slowly, week by week. Yes, your body is going to hurt from the extra fat jumping around (I experienced that too) but after a time your muscles will tone and your body will slim making it easier. Start by setting a mini-goal. Mine was to run for 30 minutes continuously. My next goal will be to increase my speed or to do 45 minutes (I haven't decided because I didn't think I would achieve it by now LOL).
My suggestion is to run for as long as you can and/or power-walk for, say, 30 minutes. Power-walking is great for increasing fitness and it's how I started to increase my stamina. My advice, and something I do myself, is that when you feel the burn, keep going for another 30 seconds before you stop. It not only helps you mentally, but it helps build stamina too.
Try doing this every second day so that you give your body time to rest, especially in the beginning or if you are pushing yourself hard. Your body needs time to heal or you will start pulling muscles etc. I pushed myself too hard too often and sustained a few and I had to take 3-4 days off each time to let them heal. Not fun!