I'm not going to let a sick person sleep in my bed.
Why don't you want a sick person to sleep in your bed?
I have this weird feeling he might hurt me in my sleep.
It would be very kind of you to let a sick person sleep in your bed, but it's understandable that you don't want them to. Sick people can spread illnesses to others, so it's best to keep them quarantined. Find a different place for them to sleep where they don't have to share a bed with somebody they may potentially infect.
I think they might be feeling better for the past few days but I am unsure.
I think it might be best to put them on the couch or some place like an extra bedroom. You might end up catching what they have if you share the same bed.