Is there a free immunization program in every state?

Generally Yes. Call your local county health department for local information regarding these programs.
Mostly For Children. Free immunization is available for uninsured children in most health Dept. Clinics in USA through Vaccine for children federal program and through most Participating Pediatrician and Family Physicians by paying a small administration cost in USA in every state. Children under the age of 19 who are uninsured are eligible. And VFC Vaccne can not be denied if family can not afford AdmFee Not for Adults.
Should be. It may not be completely free (minimal administration fee) and you may need to meet certain qualifications such as being uninsured or underinsured. Go to vaccine information. Org and click "state information" in the list on the left. Or try the cdc or your state's health department website.