RDS Oracle SE - Performance troubleshooting options
You may want to run an EC2 instance as a dev environment. Given that you don't have access to the file system on an RDS database and that you have standard edition, you can't turn on 10046 and 10053 events and use tkprof to read the files, you can't use active session history (ASH) and Automatic Workload Repository (AWR) since you need to have enterprise to use those reports and Oracle would know if you used any of those features in an audit situation.

Your best bet is to look for blocking locks in prod and use and EC2 instance to do load testing possibly using set events 10046 and 10053. There might be another tool that you can use in RDS. I don't know what that would be. You are limited in what you can do give that you are running standard edition on an RDS instance.