I believe there are different requirements for certified and creditialed employees in the CA school system.
The fact that you lied (by not including your arrests)is grounds for not hiring you, and if you had been hired and it was discover later you lied on your application, it is grounds for immediate termination.
It is important that you list the offenses you mentioned. When an employer requires arrest/conviction information on an application, they are usually only looking for certain penal codes. They are only interested in the codes that effect your ability to work as a teacher under CA law.
I doubt that you can fix this one. In the future remember honesty is your best policy. Lies and deciepts always seem to catch up with people.