This is the closest legitimate option. Scribbr offers a plagiarism checker that actually uses Turnitin’s same technology. It is (prices start around $19.95), but it is legal, secure, and private. Crucially, Scribbr does not store your paper in any public repository unless you specifically ask them to. This is the gold standard for self-checking without institutional access.
Turnitin does not provide public "free" class IDs or enrollment keys. These credentials are part of a paid institutional license and are generated only by to grant their specific students access to a classroom. How to Get a Class ID and Enrollment Key