You need to wear only one pair to keep your eyes at a stable condition. Adjust too frequently will bring damage to your sight. Keep wearing your new glasses for a week to adjust your eyes to fit them. If you still feel uncomfortable after a week, you should have your eyesight checked by an eye doctor to see whether your prescription is wrong.
Dear friend, I will not suggest you to wear both the old glasses and the new prescription glasses. The old pair of glasses is just like the expired stuffs so it can't be used again. Though it will not do great damage to your eyes and this time, but the old glasses can't correct your vision problems and give your sharp sight. It will affect your work and lead to eye strains. So you'd better not wear both old and new prescription glasses.
Usually we will not wear both old glasses and new prescription glasses at the same period. If the old glasses can help with your vision problems, you will not need to buy a new pair of glasses. It will take few days to adjust to the new prescription glasses. But if you feel discomfort after wearing the new glasses, you can have your eyesight checked by an eye doctor again for you may have incorrect degrees. I suggest you to have your eyesight checked in the morning for the result of our eyesight will be more accurate than that in the afternoon.