This behavior reminds me of the movie "Rainman," in which Dustin Hoffman's character was autistic. I'm not saying your child is autistic, but there may be some sort of sub-autistic condition that is suddenly making it more difficult for her cope with noises. (I know that when I'm tired and around lots of people talking, the buzz of conversation around me just about drives me nuts and I have to go outside in the peace and quiet to cope.)
My 3/y/o son has for the last several months been scared of ceiling fans and being up high. We couldn't place what started it, and then finally realized that we had a home movie of his uncle "sticking his hand in the ceiling fan" and joke-yelling. At the time we took the video (a year ago), my son was there and laughing uproariously. But I think that seeing the video made him think that Uncle Mark really was hurt, and now he's thinking he's going to get hurt. Has she seen any movies or TV shows (even when you think she wasn't watching) that may have shown scary noises associated with normal household appliances? I think of movies like "Gremlins" or "Poltergeist" or other even worse horror flicks. Shoot, "Monsters, Inc." may scare some kids. It's hard to pinpoint something like that (we only figured out the video-fear connection in my son because one time he happened to say something about Uncle Mark getting hurt), but you may be able to ask her if she saw something scary about it.
As far as what to do about it--tough call. I would suggest that for a while just calmly tell her before you start the microwave or whatever that you are about to do it, and if she doesn't want to hear/see it, then to go to another room. You may actually make the fears stronger by coddling her too much--she may think there is a reason why she ought to be scared if you play into her fears too much. (My mom did this w/her wheat grinder and some of my nephews--made such a big deal about turning it on that they did get scared of it.) Be careful of your tone of voice--speak positively and upbeat.
With my son, we've just not tossed him up into the air or held him high, and he's not talking about ceiling fans every day now. You can't really do that with the microwave and bathtub; but you may have some success with just making sure she's out of the room before you use it.
I would suggest that you not allow her to scream and fall in the floor, even if she is scared--give her the option of going to her room, if she wishes, but there are more appropriate ways of demonstrating fear than that.