Hi @tmiller15,
Welcome to the Instructure Community! Glad to have you here.
When you say that you invited your students to the assignment, do you mean that you changed the "Assign to" box at the bottom of the assignment from "Everyone" to a list of specific students or sections (I'm asking because "invite" is more of a term used around enrolling in a Canvas course than an assignment). If that is the case, that's the reason you don't see the assignment in student view. Student view uses a quasi-real "Test Student" user to view the course, so if the assignment is not available to everybody, you don't see it in student view, but the students you assigned it to will likely see it on their end if the assignment and course and both published.
I hope this info helps! Let us know if everything I said makes sense to you.
-Chris