How do I keep my cat out of a room I'm not allowed into?

Use the above methods (a door, a spray can of compressed air) to block the cat from entering or to make the room unappealing. If the cat enters and you need to get her out (but aren't allowed in the room) then try training the cat to come to her name. This takes time and patience, but can be done. Use reward-based methods such as giving her a super-tasty treat when she walks towards you. Put this action on cue by saying her name and "Come" each time she approaches. Eventually she will associate "Come" with getting a treat and she'll obey at will.