For labor I don't think so. They may suggest removing the tongue ring, but I don't really know. I'm sure the nose one is fine though. I watched a childbirth video at the hospital, and the girl in the video had a belly button ring in. No idea how she managed to keep it in the whole pregnancy. I had to take mine out pretty early.
The reason why they make you take out the jewelry is incase anything goes wrong and they need to bring you back to life. I had a friend that when she gave birth she went into shock and died for 2-3 min and was brought back to life, they make you take out your jewelry but just in case of any problems