Generally, to some extent, wearing glasses can modify facial features, such as the collapse of the shortcomings of the nose can be covered up a little bit. At the same time, a small nose could make it looks more refined. I think the glasses will not affect your nose. Recommend to pick black-rimmed glasses. And it is similar to the kind of non-mainstream. It can be complementary to the small nose, coordinate each other in facial appearance, and make your skin look whiter.
You can choose eyeglasses according to your face, complex, age and the height of your nose. You said you have a small nose, I recommend you can choose metal frame with nose pads, because it can adjust the distance between the glasses and the cornea. I have a same problem with you, so this is my own experience, you can have a try.
Firstly, you can buy contacts as contacts do not have frame, so they needn't the function of nose. To be honest, I have a small nose too, but I also wear framed glasses often, of course I found many problems when I wear them. The disadvantage of small nose for glasses is that the nose pads are easy to slip. So, you should select glasses with wide bridge distance, but this is not the biggest problem, the optician will test for you and make a debugger. If your face is also small, you can have the lenses small, too, because they can make your nose and face outstanding.