You need not shut down the database before the creation another database on the same system but better take a backup of the existing database so that if you make a mistake when creating the new database you might go and overwrite the existing database in which case you new database might go and overwrite you old datafiles and your old database becomes unusable
Be carefull when creating a database Plan it well before you create a database
before running the create db script please ensure the datafiles you are planning to create for the new db should not have the same name of earliar db.
2.create all neccessary directories needed for the new db as you mentioned in files.
Then you will be allright nothing will happen to your db.
all the best.
It is at all not necessary to shutdown your existing database while creating new db in the same server, but pl. make sure about the filename (like parameter files, control files etc.) and paths you r going to define for new database.