It is important to consider the purpose of the writing being undertaken. Mostly writing is a pursuit that benefits from focus, craft and discipline. An overwrought writer is no more competent than an overwrought builder, or an overwrought lawyer or whatever. Just because what you are doing is constructing something that is supposed to draw an emotional response from others does not mean to say that you should be too moved by it yourself.
Stephen King talks about being confident that the section he has just written will "get" a reader e.g. moves the reader to be frightened or tense. My mother was so disturbed by Pet Sematary that she kept her copy in the freezer and sold the book as soon as she'd finished reading it(!) If Mr. King had been similarly affected by the novel as he wrote it then it would never have seen the light of day.
Also, just because you are moved by something as you write it does not guarantee it will be as powerful for the reader. I have only ever been moved by parts of my own story when reading them back years later and having forgotten what exactly I wrote. I can quite distinctly separate out the craftsman who wrote the story and the reader who gets hit by the emotion carried in the work much later.
So, if you are seeking to write in order to inspire an emotional experience for a third party it is vital to separate the business of being the communcator from being the reader.
Having said all that writing itself can be a therapeutic and cathartic act. If your purpose is to deal with something by writing about it in the first instance then experiencing emotion as you write is perfectly valid.