A recent article in BBC News summarized a small but significant body of investigation that has been done over the span of more than thirty years. "The Puzzling Way That Writing Heals the Body," by Claudia Hammond, cited evidence supporting the hypothetical conjecture, though it also mentioned numerous inconsistencies and flaws with the research to date.
When people write about pain, they may effectively weaken its grasp over them. This, in turn, may accelerate the healing process. Even if the effect is indeed no more than "short-lived but powerful," as one scientist suggested, that should nevertheless be deemed a very positive development -- and also sufficient to warrant further study.
The entire piece can be accessed at http://www.bbc.com/future/story/20170601-can-writing-about-pain-make-you-heal-faster?ocid=global_future_rss&ocid=global_bbccom_email_05062017_future