If you call customer service they can tell you how long until your upgrade and if you phone is broke and your not eligible for an upgrade yet ask about gettting a certified pre owned phone. Your allowed one per year but you have to pay for it. I think I got my droid eris to replace my broken phone and it was $169.99+tax and you can have the equipment billed to your next bill.
If you are able to log into the Account Owner's My Verizon account, it will be on the "Home" page, you will find the words "I Want To . . ." and in those blocks you will see "Upgrade" but this is only on the Account Owner's My Verizon.