I'm okay too. I had a short walk with my neighbor and after I stayed at home. I hope you are ok.

I'm okay too. I had a small walk with my neighbor and after I'm staying at home. I'm hope so you will be ok. I'm ok, thanks ( or I am well, thanks ). I had a short walk with my neighbor and now I am staying in. I hope you are ok as well.

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. Or: I will go for a short walk with my neighbour, after that I will be staying at home. Or: I went for a short walk with my neighbour, then I stayed home. Any of those are fine, depending on when each action happened.