Rhinoplasty, when done artfully, will improve facial harmony, and should not change the apparent spacing between your eyes. Anatomically, the spacing between your eyes will not change with rhinoplasty.
It goes without being said but, the distance between your eyes is fixed. But if you were to reduce the size of your nose then a view from straight ahead will appear much different. With your nose now taking of less space on the face other areas, your eyes, could be perceived differently. It is very important to see a board certified surgeon who has extensive experience. Also walk through your consultation and have renderings made with a 3D software to get a good judgement of what your whole face, not just the nose, will look like after surgery.
A rhinoplasty procedure can accomplish narrowing the bridge, narrowing the midportion of the nose and narrowing the nasal tip, and reducing the overall size of the nose so that patient's are not so focused on their narrow eyes. It's impossible to make the eyes wider. Digital computer imaging on your nose would be helpful to understand of what can be accomplished with the procedure. For many examples and more information, please see the link and the video below
when your nasal home is removed by a very experienced rhinoplasty surgeon your eyes will be here softer and therefore slightly farther apart. This is an optical illusion and if you look at nose is done by very experienced rhinoplasty surgeons in patients with a hump the eyes will always appear softer afterward and the illusion of more distance.
You have the potential for a much improved nose to compliment the rest of your face. The distance between your eyes is fixed, but reducing your nose to its optimal condition may give you the change overall that you seek. You should consult with a Board Certified PS with extensive experience in Rhinoplasty