I assume you are using the Platform Installer since that is the only package that can automatically create a db for you. If not then you must create the db yourself and set the conneciton string.
Probably your SQLExpress is only configured for Windows Authentication, the Platform imnstaller package expects a SQL user not a windows user, so I recommend reconfigure your SQLEXpress installation for "Mixed Mode" which enables both windows authentication and sql authentication. Though if you really are not admin on the machine it may not be possible to make this copnfiguration change.
Hope it helps,
Joe