Hi Alegne,
I can only tell you my experiences as I'm no expert, but at least it's another view for you.
If you were totally unfit then running or jogging is not something to lunge into, but you have a fast walking body which is accustomed to exercise. I would say that if you want to start jogging please do so. Listen to your body as to how comfortable you feel and most definitely be aware of running in a manner which does not jar you all the way through. There was a lot of discussion a little while ago as to whether you should land on your toes or your heels when you run. I land on my toes and feel that this cushions my running far more effectively.
For fat burning the most important thing is that you are working at a comfortably raised heart rate. If you are not puffing, you are not burning fat. If you are exhausted and in oxygen debt (can not talk while running) then you are not burning fat either, just depleting your muscles. So build up the pace and distance slowly over time. The kind of puffing you're doing while running should be a pleasure, not causing you to wonder how many more steps you can do before you drop down dead

As to the stitch, this usually comes when you breathe through your mouth. Try to breathe in through your nose and out through your mouth and see if that helps. It is also possible that you have not warmed up enough and that is what is causing the stitch. Walk for a while before you start to run. I used to suffer with that a lot in the past but had forgotten all about it as I have not suffered since going raw. Thank you for making me appreciate that fact as I had not given it a thought!
I hope you come to a comfortable decision for you on both of those things.
Love
May