The only real problem you have here is tense mixing. You had a small walk with your neighbour (though you probably say short instead of small). But 'after that I am staying home' refers to a future event. So you could say:
I went for a short walk with my neighbour, now I am just at home.
I will go for a short walk with my neighbour, after that I will be staying at home.
I went for a short walk with my neighbour, then I stayed home.
Any of those are fine, depending on when each action happened.