A few suggestions.
Firstly, build up a solid base of walking
Secondly, keep your running pace down. Not much faster than a brisk walk, really.
Finally, the best way into running is a Couch to 5K program. Rather than running continuously, these programs work through progressively increasing intervals of running and walking. www.brainyweightloss.com/body-fat-percenta
Hopefully, by taking a very gradual approach to things, you will feel more confident that this program is comfortably within your limits, yet at the same time doing it regularly will extend those limits.