If the arrest was recent
Start with the county jail
In Tennessee, someone who was just arrested and not released is held in the COUNTY JAIL run by the county sheriff (Tennessee has 95 counties and no unified statewide court or jail portal), not a state prison, so TDOC's FOIL will not show a brand-new arrest.
Tennessee participates in the national VINE system (Tennessee VINE), a free way to check custody status and register for alerts by phone, email, or text (search at vinelink.com).
Many Tennessee county sheriffs also post an online jail roster or 'inmate population' lookup (for example, Davidson/Nashville, Shelby/Memphis, Knox/Knoxville, and Hamilton/Chattanooga counties).
For a very recent booking or bail information, call the county jail's booking or records line.
Jails are run by the sheriff in each of Tennessee's 95 counties, and many post an online jail roster or inmate-population lookup. Use the county sheriff's roster or Tennessee VINE, and call the jail's booking/records line for a recent booking and the bail amount.