I created a story map in my personal account, but I want to transfer it to my work account.
On the item details for an item in an Organization, the admin can change the owner of that item to another user in the same organization. That doesn't apply in your case though because you want to transfer ownership between a Public account and an Organization.
Using the ArcGIS Online Assistant tool: ArcGIS Online Assistant you can copy ArcGIS Online items such as apps, including story maps, from one account to another, which would work in your case. After opening the tool, and signing in, you can either browse/search your content to find the story you want to copy, or search all of ArcGIS Online if you want to copy an item that you don't own. Then choose "I want to > Copy Content". You can then sign in to the account you want to copy the app into. Note that in the case of story maps where you have uploaded images directly into the story, those images aren't included in the copied story: instead the copied story still references the images in the original story, so you'd have to upload them again into the copy to make the copy self-contained (i.e. so you could delete the original story. Also if you are using Story Map Tour, Shortlist or Crowdsource, which have internal references to the web map in which the places they display are stored: note that if you copy those apps the copy will still reference the original web map, even if you also copy that web map.
perhaps the faq would be a good place to look in case this covers your situation
Frequently asked questions—ArcGIS Online Help | ArcGIS
I don't have any experience with Story Maps specifically, but there are many admin tools for ArcGIS Online that you may want to check out. one of these may have a tool that will work (and most of the tools are free)
Resources · Esri/ago-admin-wiki Wiki · GitHub
And an older blog that talks a bit about these ArcGIS Online admin tools available on GitHub | ArcGIS Blog
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