Being ill can cause some very strange dreams. Usually when we are ill we feel very vulnerable, and want comfort and protection. Your Dad was probably your safety net. Someone who made you feel safe and secure.
Chairs - represents passivity, relaxed attitudes, inactivity, receptivity, openess, rest and waiting. That your Dad was trying to rescue you suggests it's likely that you are overwhelmed or feeling incompetent in an important area of your waking life.
You're being ill would leave you overwhelmed by just about everything.

I hope this helps, & I hope you feel better soon.
Hugs & Hope,
J