There is a difference between writing and speaking. If when talking you say "Whos going," the listener will likely hear it as
Who is going. But if you write who's, the reader is apt to think it is a possessive, as in
Who's key is this? In general, it is easy to over use contractions. Only use them when they are very commonly used. And if you like, you can never use them, except, I suppose, if the teacher wants you to.