Go to Settings/Apps. Find Skype. Force Stop. If that fixes it, Skype wasn't releasing the mic.
If that doesn't fix it, Skype has nothing to do with it. (And it probably doesn't, because it uses the same mic as the speakerphone.) Then you'll have to look further. Use a very strong light. Look into the mic hole (the one n the bottom - look in the manual if you can't find it.) Use a magnifying glass if you're older than about 20. See if there's any dust or lint i there (they're good sound absorbers). If there;s anything in there, use a small, pointed wooden toothpick to pick it out.
If not, the mic could be bad and you'd have to ave it replaced.