It is normal to get peripheral distortion when your prescription is too strong or when your glasses frames are too large. You can get used to them as soon as possible because the eyes adjust quickly. If you can't adapt to them quickly, you should take your reading glasses back to the place you bought them and have your glasses checked. The worker there will help adjust your reading glasses to minimise this effect.
It sounds you may have strong prescription. Usually. Peripheral distortion will happen in the following cases. First, it will happen when the prescription lenses made stringer. Second, it also becomes more apparent if the eyeglasses frame you choose is larger. You may takes a few days to adapt the lenses. If it still distortion, you shall buy a new pair of reading glasses instead.