Expungement is basically a dismissal so that would not really help you. If you were not convicted of any charges stemming from the arrest then you can file to have your arrest record sealed pursuant to California Penal Code section 851.8. In order for the judge to grant the sealing request, there must be a determination of factual innocence. This means you must show there is no reasonable cause to believe you committed the offense you were arrested for. This is more than filling out a form. Also, if you wait longer than two years to file the motion to seal the arrest then you must show good cause.
Expungements are for convictions. Since your case was dismissed, you were never convicted you do not need this. You can petition the court to have your arrest record sealed. To do this, however, you need a determination of factual innocence. You will need to retain an attorney to help you with this. You should not delay. If you wait until the two-year limitations period expires you can only succeed if you can show good cause for the delay.