No, it doesn't mean 'possibility'. You asked an almost identical question a few days ago. The answer to this question is exactly the same as to your previous question. Did you see the answer I gave you? You did not acknowledge the answer, so perhaps you didn't see it, so I'll repeat what I said: This has nothing to do with possibility. In contexts such as this, the modal 'should' indicates advisability: it's an issue of whether something is a wise or sensible course of action or not. In this situation, you are sick and you are working. However, you think that this is maybe not a good thing. You suspect that it is not prudent to be working while you are ill: you think that you have probably made a mistake and that you ought not to be at work. You shouldn't be working today: you should be at home in bed. I hope that this is clear now.

No, not really. It means that you better not be working, or that it's better for you not to be working. So even though you might be able to work (have possibility to work), it might be better for your health not to work. So "should" is more like ~으면 (안) 된다, ~어야 된다, or ~면 좋겠다 in Korean. I quess it would be something like this in Korean. 난 아프다. 오늘 일하면 안 되겠다. or 난 아프다. 오늘 일하는 게 괜찮을 지 모르겠다.

Thank you. :)

I am sick. I am not sure if I should work today or I am not sure if I should go to work today.