Solution 1:
Create an event receiver on ItemAdded, so whenever a student uploads a document, the event receiver fires and breaks the inheritance and assigns explicit permission to the student. That ways you can assign permission to items to whosoever you want to. For code to implement this you can follow
http://blog.sharepointclick.com/2013/04/programatically-breaking-inheritance.html
Solution 2:
1.Create a view within the document library with a filter Show items where created by is [Me]
2.Set default view to this view within the document library and remove all other views
3.Control permissions in such a way that the students cannot change views so they will only see the documents that they have uploaded
Hope this helps. Let me know if that resolves your problem or we can think of some other solution.