I know you said you were training for a half marathon, but have you experimented with muscle training? I was in sort of the same situation as you, and when I took up weight lifting, a switch just flipped on and I stopped obsessing over a lot of things. There's just something about working your muscles to the point of failure that feels great and distracts me from feeling down. It's definitely not for everyone, but calisthenics might be worth a try sometime.
If not physical activity, just any hobby could help you get your mind off of things. I'm not a professional, this is just my opinion.