Small, specialty magazines are more likely to really want free copy, as long as your story fits their theme (say, 'Walking in the Laurentians', or 'Reptile Pets').

Speaking from the POV of a small mag, which might have only two or three employees (publisher, editor, designer), all of whom do double duty reporting, proofreading, picture taking, etc., a well written story, preceded by a phone call/email exchange, is really welcome. Including a picture or graphic is nice.

Something with health or medical themes, however, would be looked at very carefully. Backup documentation from a medical doctor or a hospital would ease your way.

And yes, editing is almost certain to be done, usually for length. A good layout person will edit seamlessly, a poor one can make the story senseless, and can even change the point you were trying to get across. Read a copy of the zine before sending your story.