adriannajam With the game already downloaded to your drive, you could tell the EA App to "download" it to the same location. The App often simply verifies the files and finalizes the install process, although sometimes it insists on redownloading part or all of the game. (I've had mixed results when testing.)
While using your friend's computer, how were the download speeds? If they were what you'd expect, that suggests the problem is your computer, but the question is what specifically. I'd like to look over a dxdiag next. Click Windows key-R, enter dxdiag in the run box, wait for the scan to finish, click "Save all information," and save the file to your desktop. From there, you can attach it to a reply using the paper clip (Attachment) icon included with the other formatting buttons.
Please also let me know whether your computer has another port you could connect the drive to, and if so, whether the download speeds are better that way. It's possible the port itself has an issue.