You want to know how I did it? I made everyone else do it for me. I was getting married 6 days before we left and with the wedding and moving there was no way I could have kept my cool. So I got a wedding planner. I made her do everything for me. I was living at home and didn't have many bills in my name, but those took only a few hours to take care of and my dad did most of them. I had my car which I found hard to sell and so I left it with my folks, who used it for awhile, but eventually sold it a few months after I left.
I had a bedroom, so not much stuff. But I packed it all. I only brought my clothes and a few knick-knacks with me. I really wanted to simplify things. (Plus, we plan on moving back in a few years, didn't want to pack it all up and ship it back.)
I was mostly in a daze the entire time, but the moments I did feel overwhelmed, I just told myself to get through it because it wasn't going to last forever. So that's what I recommend. Stop for a moment and tell yourself that it won't last forever. You'll get through it and when you do, you'll look back at it all as a crazy time, but well worth it in the end.