Can my lip ring and nose hoop be worn during Laser Resurfacing? Or will I have to take them out?

Anything metal can reflect the laser beam to other areas, so needs to be covered or removed.  If you are treating those areas, then just take them out.  If not you can cover them with a wet gauze pad.

Yes, you will need to remove your piercings from any area that is being treated with the laser. Not only will jewelry block the laser but it can also scatter laser energy to areas that are not meant to be treated. The laser can also damage whatever material your jewelry is fashioned out of. Stephen Weber MD, FACSDenver Facial Plastic Surgeon

I'm not sure if you are having your entire face treated with laser resurfacing or just parts of your face.  If the area around your nose and mouth are going to be treated, then you most likely would need to remove your lip ring and nose hoop, as these would be in the treatment area.