MOHS surgery per se does not cause collapse of the nostril, nor does the needle used to numb the area result in this. The only thing that can cause nostril collapse is removal of the cartilage that supports the nostril during the surgery. This is sometimes required to get a good margin of excision. This your surgeon can tell you. Also, the collapse is visible from outside compared to the normal side. If this is not the case, then it is probably due to secretions inside causing blockage.