What do you call a sick person who is lying in bed?
bedridden (ˈbɛdˌrɪd n) TFD
adj. confined to bed from illness.
Try this one on for size.
I am currently bedridden and can't help you with your homework.
'Laid up' is possible. "I can't come in to work this morning. I am laid up with a bout of malaria".
As a native speaker, I might use bedridden for a period longer than several days, but the term is not often used in casual conversation. I would use "sick in bed" if it's just a few days, e.g:
I am currently sick in bed and can't help you with your homework.
"Laid up" isn't used very much where I live (New England). It's probably more common in other regions.