We backed a car (don't ask!) into the brick front wall of our porch. The porch is a waist-high brick enclosure built on a carport pad ages ago, with a framed and screened upper part, and a regular peaked roof on top. The brick wall runs from the corner of the porch to a doorway opening, about 6 ft. It separated at the corner, and slid 9 inches inward. There is a substantial brick shelf or seat on the inside side of the wall, adding to the bulk and weight of the wall. The only brick damage is at the corner, and most of that is simple separation. So, how do I move it back? I put a 4x4 against the base and whacked it 10 times or so with a 10-lb sledge, but it won't move that easily.
If you can get purchase on the wall with a rope and have a hitch on your car the poetic justice approach would be to attempt dragging it back into place. :-) But I expect this will just pull it off the carport pad and into your yard.
I suggest you contact a brickmason. From your description it sounds like there is a screened-in porch supported by that wall. You will need a mason to repair the wall or risk losing the porch. They might attempt to drag it in place and patch it but I doubt that. Most likely they demo the wall and build you a new one.