You've got something a bit confused.
You can't have two primary keys. You CAN have a primary key which consists of more than one column.
Normally I avoid having tables with a multi-column primary key, and instead add an artificial meaningless (autonumber) ID, even if it's not used anywhere (it typically isn't).
In any case, you can have more indexes. Creating a primary key always puts a unique index on the set of columns in the PK, but it does not stop you having indexes on other sets of columns.
Indeed, if you're searching on part of the primary key, an index on the whole PK won't be useful, so you might want to add another one.
Mark