Legal Question in Criminal Law in California

I'm sorry for what happened.

No, you cannot bring criminal charges. That is up to the prosecution. You can make a police report and they will submit it to the district attorney for review.

The District Attorney is the one in California who has the discretion of whether or not to file criminal charges.

You and your mother need to retain attorneys in order to recover the substantial money to which you may be entitled. Unless the police responded to the accident scene and the other driver admitted to texting while driving there will be no criminal charges, and whether or not there are criminal charges will be far less important to you than the need to recover money for your medical bills, lost wages, your child's future medical bills, and everyone's pain and suffering. Just sue them to recover from their insurance company (if any). Watch out for legal time limits.

Only Police and DA's file criminal charges. You and your mother get to file a lawsuit, but you face the test of whether it is practical to do so. If the case has MERIT [reasonable likelihood of winning] which you seem to have with his admission of liability, VALUE [substantial recoverable financial damages], and COLLECTABILITY [defendant with assets or insurance coverage], all of which are necessary for a successful claim and case, then feel free to contact me; I'll be happy to help you. Immediately try to determine if he has insurance.