Are you on one of the newer boxes (after Linode's move to SSDs and newer CPUs), or still on a pre-upgrade box? If you're still on one of the older boxes, then the free upgrade could get you a lot more breathing room. If you're on one of the newer ones, then that's not going to be a great help

Ignore vonskippy, he's the resident curmudgeon. Splitting your webservice and database are the natural first step when increasing capacity. It's the logical first step in expanding horizontally, and it's the easiest one too. Once you've got your database on its own 4GB box, don't forget to tweak MySQL's settings to take advantage of the RAM. You can start with the biggest sample file that MySQL ships with (my-huge.cnf, meant for servers with 1-2GB of RAM that mostly just run MySQL), and then you can use mysqltuner to help tweak it from there.
Note that you need to let the MySQL server gather statistics before running mysqltuner. The idea is that you let your database server run with real load on it for 24 hours or more, and then you run mysqltuner, which will look at the statistics the server has gathered and suggest changes to your config file based on your workload.