I'll say first that I'm not an advice extraordinaire or anything.
Working out to deal with emotion, to me, doesn't really have to be a bad thing. It can be a good thing so long as you're doing it because it makes you feel good. If you get upset and go to work out as a way to physically beat yourself up about your emotions, that's not really so great.
Maybe if you're feeling blue, you can go for a walk, not a run. It's still exercise, can be tiring, and is still good for you. Walking around can also be a great way to clear your mind, which should help. Since you decide to go on an empty stomach, you should bring along a lunch or snack for when you get tired, and some water. Since you're not running, carrying a shoulder bag won't be a problem. I guess carrying a bag adds a little resistance too?
There's my two cents. I hope it helps in some way. I hope that whatever is making you unhappy will reveal a positive side as well!