How are you with friends, do you have any where you're living? It would be nice to hang out, you could even go to a friend's house, or somewhere you feel ok, like a library or cinema maybe? Not too many people, less busy than a shopping mall, and you won't be alone.
Maybe a club/group could be something you'd consider? I don't know what's available where you are, but a group with other people around your age, where you maybe visit places or do a certain activity, you could really enjoy that. Or maybe a class, say if you want to study something like a language or a craft, that could be fun and you're out but with other people, which might make you feel safer?
Because you're so scared to actually leave the house, maybe start small. Do you have a garden? Is there a shop nearby that you could work your way up to going to? Give yourself little tasks, where you know you can come right back home if you start to feel unsafe.
Good luck, hun x