It does happen that people exaggerate or fake injuries after a crash, but the good news is that their claim has to be backed up with medical records, evidence, and an insurance investigation. If you think the other driver is not being honest, focus on documenting everything you can such as photos, witness statements, and the police report, then give all of that to your own insurance company and let them investigate the alleged injuries and possible fraud.
From there, your insurer and, if needed, your attorney can challenge inconsistent stories, request medical records, and even push for an independent medical exam if the case escalates to a lawsuit, so you do not have to confront the other driver yourself.