You do need another small database to keep the repository of the monitored databases. OEM can be instyalled on your workstation as it does not require much of space but you are right that you will have to keep it running all the time if you want to monitor your database constantly.
In that case write your own scripts (use dbms_pkgs) and set the jobs in CRON to run repeatedly (or I think with DBMS_PKGS you don't even need cron scheduling).

- Rajeev