Maybe your old glasses are too loose for you. So when you choose the new glasses, you shouldn't choose the same size as your old one. In this case, you should go to see an optometrist to get an eye exam. The optometrist will measure your glasses size which include Bridge Width, Arm Length and Lens width. He will measure your PD, too. After that the optometrist can make glasses that suit your face correctly. You can ask your optometrist for a copy of your prescription and then you can choose the right size of plastic glasses.
Just Try on some glasses frames in a eyeglasses stores and pick up the best suitable one. If you don't want to buy from local store but from online shop, You can refer to your the size of your old eyeglasses. Look at the inside of your old glasses temples, you can see the sizes of the eyeglasses frames. Then you can buy new glasses refers to that frames sizes. Good luck.