Protecting Students from Worthless Degrees Act This bill makes an institution of higher education (IHE) ineligible to receive federal student financial assistance if it fails to meet certain requirements, and it requires an IHE to make certain certifications about its gainful employment programs. Specifically, an IHE that offers a degree or certificate program to prepare students for entry into a profession that requires licensing or certification as a precondition for entry is not eligible to receive any federal student financial assistance unless (1) a student is fully qualified to take the required entry examination or be licensed or certified for the profession upon the successful completion of the program, and (2) the institution provides timely placement for all of the academically related pre-licensure requirements for entry into the profession (e.g., clinical placements or internships). An IHE must also certify that each eligible gainful employment program meets specified requirements, including approval or accreditation by a recognized agency and satisfaction of applicable educational prerequisites for professional licensure or certification. If an IHE does not satisfy such prerequisites, it must notify a student who intends to enroll in the program and obtain a handwritten acknowledgement from the student that they wish to enroll. Lastly, an IHE that offers distance education or correspondence courses must be legally authorized within each state in which its enrolled students are located.