MySQL Performance Schema
The slowlog is my favorite means of quickly identifying performance problems.  (I don't care for the performance_schema.)  Set long_query_time=1 globally, turn on the slowlog, wait a day, then look at the log

The slowlog can be sent to a file.  If you don't have access to the filesystem, what version of MySQL you are using?  In newer versions, the slowlog can be sent to a table, thereby avoiding the need for access to the disk.

If possible, use pt-query-digest to summary the slowlog file.  The first few queries will be the "worst".  We can help you speed them up, possibly by adding a "composite" index, possibly by modifications to the query, possibly by schema redesign, etc.