"FTL: Faster Than Light" or "The Wolf Among Us" are good choices to play when sick. Each offers relaxed but involved interaction with a pause game feature for abrupt bathroom breaks.
The mission in "FTL: Faster Than Light" is to deliver important information to the other side of the galaxy while outmaneuvering a rebel fleet that wants you dead. Game play consists of making hard choices and delegating orders to your crew to overcome randomly generated challenges. A murder mystery set in a world were fairy tales have been forced to immigrate to New York City, "The Wolf Among Us" features rich storytelling, interesting characters and slow-paced, quick-time event style action.