Brushing everything else aside, maybe you could try walking to the end of your street and back once or twice a day? And then gradually increasing this as the days go by.
The trouble with not leaving the house, and being at home all day, is that things fester and grow till they seem much bigger problems than they otherwise would be. Things must be going round and round in your mind all day, with absolutely nothing to distract you from what's upsetting you.
How far from the shops do you live? I think you said you live within walking distance?
Maybe as you get more confidence, you could aim to go to the shops everyday and buy just one thing, rather than buy in bulk. That way, things won't be too heavy, and it won't be as stressful, because you could literally be in there for a short time.
I think it would help you to set small achievable targets and aim to conquer them. The interaction with other people, and the change of scenery will help. There is nothing more depressing than being cooped in and looking at the same four walls for weeks on end.
Good luck, OP, I'm sure you can do this. 