Not trying to freak you out but this is exactly what turned into an eating disorder for me. They were so similar. Feeling depressed and anxious and feeling hungry. So I would starve myself on purpose until the hunger was stronger than the other feelings in my chest/stomach. It gave me something else to focus on and the physical pain could outweigh the emotional pain at a certain point. And the thoughts about food would drown out all the bad thoughts. I didn't even realize I was doing it for a little while I just fell into doing it. Then from there it turned into an obsession over food and calories as a distraction from my life. It took forever to break the habit and I still fall into it sometimes.
I recommend just eating 3-4 smaller meals throughout the day even if you don't know if you're hungry. And if I Meditate for about 25 minutes I can feel the weight lift off my chest for a little while too. Meditation and mindfulness have really helped me a lot. Taking a break from feeling all these emotions sometimes is really helpful.