Upload local WP site to Host Gator

I started building a WP site on my MAc here at home.

Then I purchased hosting at Host Gator. Now I want to upload my existing site from my computer to the remote server.

Installing WP on Host Gator is a cake walk. My issue is I want to upload what I have on my machine to the server. I have been at it for nearly 3 hours and have created and trashed several databases in the process. Does anyone know of a way to upload my WP files, and my data base to the remote server without having to start from scratch???

Any help is greatly appreciated!