Tracing oracle database
Tracing is difficult in Oracle Database for several reasons: 


you need to identify the involved database sessions which is more or
less easy 
you need to use DBMS_MONITOR package (only granted to SYSDBA
by default) 
you need to have access to the raw trace files (they are
generated on database server side - see V$DIAG_INFO view)
you need to use TKPROF on the raw trace file to have something
readable (TKPROF is part of Oracle Client but not Oracle Instant Client).


If you need to have only SQL statements without execution plan and detailed timings you could modify your code to enable SQL trace with "ALTER SESSION SET SQL_TRACE=TRUE" (raw trace file generated on db server side).

If you have your dedicated database instance (like Oracle XE) you could just enable SQL trace on database level (ALTER SYSTEM SET SQL_TRACE=TRUE) and get all trace files.

Here is one of the best summary of SQL tracing options in Oracle:
https://oracle-base.com/articles/misc/sql-trace-10046-trcsess-and-tkprof

You don't need OEM to enable trace but you need DBA privileges or to work with your DBA to use SQL trace.