I am a HORRIBLE runner. Somehow I keep chugging along though.
If you can't run, then walk. Start out training by doing a walk/run.
For example... take a watch with you and run 30 seconds... then walk 3 minutes. Something like that. Pick an interval that works for you.
Now when you run... don't go all out... just do a simple jog. Take it easy. It's OK.
As you start to feel your shorter run segments are becoming easy... move to longer run segments.
Ease into running. It will come with time.
Also, go get fitted for proper running shoes based on your stride. Might help with shin splints.
Good luck!
"Life is not a journey to the grave with the intention of arriving safely in a pretty and well preserved body, but rather, to skid in broadside thoroughly used-up, totally worn out, and loudly proclaiming: WOW WHAT A RIDE!!!!"