The Short Version
The claim is well-supported. Multiple credible medical sources, including the Cleveland Clinic and ENT specialists, confirm that suppressing a sneeze can redirect pressure internally, potentially damaging eardrums, sinuses, throat tissue, or blood vessels. The claim uses "can have," which is a possibility statement — and documented case reports plus established physiological mechanisms are sufficient to validate it. While severe outcomes are rare, the possibility of negative health effects is real and medically recognized.