Unfortunately your post is confusing. You tried to have the ticket issued at the airport? Why didn't you call Skymiles and have the ticket issued over the phone or do it online?
All I can say now is to continue to call Delta until you get the answer you want. If you indeed "paid" for a round trip ticket with the miles, you are due a round trip ticket. But if in the haste and hectic, you only booked the one-way using your friend's miles, then a one-way ticket costs the same number of miles as a round trip ticket and you are SOL. It might be an expensive lesson to learn.
After check in I almost always scoot off to the side and review my travel documents - do I have the right boarding passes? are they all in my name? Is my frequent flyer number correct? Once I was handed the boarding pass for someone else!
John