As of October 1, unvaccinated students do not have to quarantine after travel within the United States. They should get tested 3-5 days after returning from travel (this can include the SHIELD screening test).
From the Illinois Department of Public Health:
In general, Illinois continues to recommend that people follow the CDC’s recommendations for domestic and international travel, including that people should delay domestic travel, and not travel internationally, until they are fully vaccinated.
Additionally, the CDC’s guidance for schools is that in- person learning is a priority. Thus, school-aged children who are not fully vaccinated and must travel do not need to stay home and self-quarantine after travel; they should continue to attend school in- person. School-aged children who are not fully vaccinated and must travel should get tested 3-5 days after travel, monitor for symptoms, and follow the IDPH guidance for if they test positive or if symptoms of COVID-19 develop.
Schools should follow local guidance for travel restriction that may be more stringent.
In a webinar for schools on October 1, the Cook County Department of Public Health confirmed that they are following IDPH guidelines; therefore, D34 students do not have to quarantine after domestic travel and should test 3-5 days after return.