LION: Literature Online provides online texts of many English and American literary works with a search mechanism to facilitate text analysis. From the main LION menu, choose Texts to search for words and phrases within a specific work or group of works. LION also lists literary works published in journals. To find these, choose Criticism and tick the box to limit to "literary works".
Google Book Search provides online full text of many books, including anthologies of short stories. There may be limitations on viewing pages published after 1923, but some short stories may fall within these limits.
The MERLIN Catalog lists collections of short stories. Search by table of contents to see if a specific story is listed, but note that MERLIN doesn't provide the table of contents for all books.
The Short Story Index (Ref. Z5917.S5 C62) fills the gap by listing stories and showing where they have been published. You can also use this index to identify short stories by topic or theme.
Also try putting the title of your short story into Google Books. You may not be able to access your short story through Google Books, but it can help you find what collections contain that story.
To browse contemporary short stories, do a Subject Search in the MERLIN Catalog. Suggested Subject Headings: