I've otosclerosis. I am 39 weeks pregnant n the hearing has worsened. Will an induced delivery worsen otosclerosis?

No. It has long been held that hearing loss in otosclerosis worsened during pregnancy. Recent data disputes this. Method of delivery should have no effect on hearing loss.
Unlikely. Though it was once thought that pregnancy may worsen otosclerosis and it's related symptoms, newer research and more recent studies do not support that theory and found no such effect. Good fortune and good hearing on your delivery.