........ We found part of it was attached to the back of the fireplace with a wire mesh. I'm not sure if I can just drywall over this or not.
The International Building Code has new minimums on fireplace clearance:
from:http://www.rumford.com/code/IBC06.html 2111.11 Fireplace clearance. Any portion of a masonry fireplace located in the interior of a building or within the esterior walls of a building shall have a clearance to combustibles of not less than 2 inches (51 mm) from the front faces and sides of masonry fireplaces and not less than 4 inches (102 mm) from the back faces of masonry fireplaces. The air space shall not be filled, except to provide fire blocking in accordance with Section R1003.13.
There are also Exceptions listed that may make your existing configuration OK. It's best to get a licensed fireplace contractor to look at it for an OK before any drywall work,