Re-reading your story before you publish it, is a big part of good writing, because that way you can get rid of all the unnecessary clutter in your story. You can always ask friends and family members to read your story, to sift out any errors and typo's that may still be in your story. Just make sure you ask someone who reads a lot and knows how a story is supposed to work. If you are writing in a language that is not your primary language, let someone check the story who is fluid in that language.
Sometimes you need to cut out a lot of junk from your story to make it work, but if that's what it takes to get it right, then so be it. I am working on a story for my course and i have re-read it now several times and edited it. I am also bound my a maximum of words, so that makes it a bit harder, but doable.
So keep editing your story until you are happy with it, and then let someone else read it to finalize it.
Happy writing all!