Hi
It sounds like your backup file is attempting to recreate the database itself. That is not necessary because the database already exists.
You need to open it in a text editor, like Notepad on a PC, and see if you find a line that says CREATE DATABASE. Remove that line (make a a copy of your backup file before you start changing anything).
You also want to see if your backup file has a DROP TABLE command before each CREATE TABLE command. Your tables already exist in the database, so if there are no DROP TABLE commands in your backup file, you are going to see TABLE ALREADY EXISTS error messages. The easiest way is probably to just delete the existing tables in phpMyAdmin, since the DROP TABLE command deletes it anyway. Then running the backup script will create the tables again, and insert the old data into them.