Two or more defendants can be charged in the same case. They will have the same case number except for the last two digits, which differentiate multiple defendants. For instance, in Los Angeles County, a felony case number might be BA123456-01 (for the first defendant) and BA123456-02 (for the second defendant).
Your attorney can move for separate trials, but will need to show how you will be prejudiced by a joint trial. The fact that your co-defendant has a record will probably not be a sufficient reason because the court is concerned about "judicial economy" - i.e., unnecessarily spending more money to prosecute each defendant separately - and the court will give instructions to the jury as to what evidence relates to which defendant.
Ms. O'Conner is correct about the procedure to follow but under the facts you state there is no way you'll be severed from your co-defendant. You need a lot more reason than what you have for severance. One of the strongest arguments against severance is that the same evidence will be used against both of you.