You are correct in your assumption that there is a better way. What you need is the "relational" in relational databases.
You need only 1 table for the sessions. This table contains columns for the session data, probably a unique ID (use auto-increment) and most important of all, one field where you store the ID of the user the session belongs to.
This is called a one-to-many relationship, because one user can have many sessions, but each session is coupled with only one user.
If you use MyISAM as the DB engine, you will need to keep track of the IDs manually, but if you choose InnoDB as the engine, you can use foreign keys.
You can read more about foreign keys in the MySQL documentation: http://dev.mysql.com/doc/refman/5.1/en/innodb-foreign-key-constraints.html