Quetext offers a free tier that lets you check up to 500 words. For longer essays, their Pro version is very affordable ($9.99/month). It uses DeepSearch™ technology to find fuzzy matches (paraphrasing) that basic checkers miss.
However, Turnitin does allow instructors to enable a feature called (for Microsoft Word) or "Similarity Report" for students to use within the university LMS (Canvas, Moodle, Blackboard). This allows unlimited re-submissions until the due date. turnitin free class id