No, in order to enter Mexico or the US by air, both you and your child will need a passport.
If you are US citizens, you may be able to get a passport in a hurry at the San Diego Passport AngencyAgency; be sure to follow all the instructions on their page regarding appointment scheduling and necessary documentation for both you and your child.
If you are Mexican citizens, you can follow up with the Consulado General de México en San Diego for advice. If you are some other nationality, you will have to figure out the closest consulate of your country to you and go from there.