You are most likely trying to go too fast, too soon. You probably have an image in your mind about what it means to be "running" and are trying to meet that, which is where the problem starts. (Well, it was for me, anyway)
I would recommend slowing down. I am a slooooooooooooow runner. When I started, I was barely going faster than a brisk walking pace.
Barely. I think that even power walkers could have passed me!
I'm not that slow anymore, but neither am I as fast as others who are my height, age, or weight. It doesn't bother me, though, since I know I am doing the best that I can. I don't compare myself to other people, so I don't get discouraged about being slower or not being able to run as far as other people.
Anyway, you will find that as you lose weight you will just naturally pick up speed. Also, as your body becomes more efficient about running, you will increase your speed. The speed will come. You just have to be patient with yourself.
Also, don't expect to go out and run for miles, or even a couple of blocks, without building up to it. You have to work up to it, and the best way is to do the walking/running intervals. Walk for a bit, run for a bit, repeat. As time goes on you can start increasing the distance you are running and shorten the distance you walk, and one day you will find yourself running your whole route!
Lots of people recommend the "Couch To 5K" program (I'm not sure about exactly what it's called), which can help you out. I believe it basically tells you the same things I've mentioned, but it gives you a specific plan to follow.
So, my advice would be to slow down, be patient with yourself, and just keep chugging along.
