Well, according to your description, I can see that the acetate glasses is not suitable for you head size. However, you should know that most acetate glasses could be adjusted to difference head sizes. You should follow the instructions and see what could be done. But if this does not work, you should just get another pair of glasses that is suitable for you.
Well, when you buy a new pair of glasses, it is normal to have it bigger or smaller. And this will make you feel so uncomfortable, for they can slide off from your eyes. To adjust them, first, you can put on your eyeglasses and, while looking in the mirror. In this way, you can check precisely. And then just be careful when you tighten the screws on your eyeglasses. By the way, you should adjust the arms of the eyeglasses carefully and slowly with needle-nose pliers. If they are still bigger, maybe you can go and console it with a professional person. They can just solve the problem for you.