This sounds risky to me - you should contact Emirates to make sure your booking remains in their system. Travel agents are not always reliable.
As you are Skywards Blue member, there should be no problem reserving your preferred seat in advance.

Concerning the missing booking in your "My Itinerary" screen, I guess the travel agent got a new reservation code by booking the Business-Class tickets. If he didnīt add your Skywards number to the booking, the itinerary wonīt show up (in that case, you have to contact EK via the provided online form).

As a Skywards member, you have waitlist priority, however the status passengers go first. I think, EK will do their best to get you onboard.

Have a nice trip ^