Ok I had to figure it out myself and here's the process for anyone else who might need it:
In order to switch instances without losing your data, you need to save an image. Go to the Amazon EC2 Dashboard and find your current running instance. Right click on it and select "Create Image (EBS ABI)". A screen looking like this will show up:
Choose a name for your image and deselect "Delete on Termination". Then click save and click Yes, Create.
You can view your image by clicking "AMIs" under the Images tab on the left sidebar of the EC2 Dashboard. It will take 5-10 minutes or so to save it. Once it is done, right click on the image you saved and click Launch. You will go through the steps then to open a new instance (the instance will be on the same server and OS you chose). Then just terminate your old instance and viola, you have a new instance with your old data opened!
Note: it will cost money to do this so I suggest you delete your image once you've created your new instance. It was under $2 for me though so yea.
Edited by cuttingedge, 01 November 2013 - 11:40 AM.