Can you sue if my son choked on plastic inside of a corn dog from the schools lunches?

That depends on if the school was the one making the corn dogs, or if they bought them from a bulk supplier. If it's the latter, you could most definitely look into filing a lawsuit.

Also, if any of the faculty noticed your child choking, but failed to administer aid in the potentially life threatening medical emergency, you can file for lawsuit against the school and faculty member both. You can also charge the faculty member with child abuse (failure to administer first aid in an emergency situation) and have them put in jail (possibly 20+ years in prison). If they are a teacher, they can lose their teaching liscense, which can prevent them from ever teaching at a school again.