Hi I am Doctor Trace and I hope I can answer your questions. It is possible to burn the cornea during cataract surgery. These types of burns usually heal up without sequelae in about two to three weeks. If there is swelling associated with the burn, it could take a little longer. With the older types of phacoemulsification machines, many post op patients had burns of the iris and cornea. They all heal well for the most part.
Just be patient and do what your surgeon instructs. If he has been doing cataract surgery for a while, he has treated this condition before and can best judge how to heal your cornea. Trust him and be patient.