You should file the paperwork in the court where the "main" case was decided. If the only case you have has a file number starting with BY, then yes file your paperwork there. I am including a link to some self-help resources on changing child support. Hopefully, this will be a good starting point for you.
You need a form packet that you can get from the nearest Superior Court. Just ask at the family law facilitator if you can not afford an Attorney and they will help you fill out the forms
My name is Stephen R. Cohen and have practiced since 1974. I practice in Los Angeles and Orange County, CA. These answers do not create an attorney client relationship. My answers may offend I believe in telling the truth, I use common sense as well as the law. Other state's laws may differ.. There are a lot of really good attorneys on this site, I will do limited appearances which are preparation of court documents it is , less expensive. However generally I believe an attorney is better than none.