Is it possible that my fear of ghosts is rubbing off on my 3 yr old because every night shes afraid of "monsters in her room"?
It's very possible. Young kids are extremely intuitive and very empathically atuned to their parents emotions and fears. But it's also very normal for kids at that age to go through a fear of the dark, and "monsters" are a common representation of a child's fear.
It's always most useful to work on our own fears and emotional well-being, because it is in that way that we help our children the most. When we are calm and happy, they are at their very best. Parenting can be very stressful and hard sometimes, so you can't be too hard on yourself for every negative emotion you have - just work on yourself as best you can, and be kind to yourself.
EFT/Meridian Tapping can be an excellent way to quickly and permanently eliminate fears and phobias. You can learn about it here.