They do connected from each other, people's organs are all connected by nerves and blood vessels.
The serious eye disorder may cause the discomfort of your nose. Actually, my mom has nasitis then she always feel uncomfortable of her eyes, they always full of liquids or discharges. I mean the theory is the same for your situation.
However, slight eye disorder such as eyesight problems won't be harmful for your nose.
Once you have eye disorder, you need to cure then as soon as possible, do not let the bacterium be transferred to the other organs.
Ok, I can see that you are worried about your health problems due to your eye problem. Anyway, it is true that your nose is connected to your eyes closely because they are so close to each other. But more often than not, it is nose problems that give rise to uncomfortable feelings to your eyes, such as sinus infection or allergic nose. Anyway, try to take care of your health problems before they get worse.
No, people's eyes are not connected to nose. You body has many parts of organs which containing different cells and they do not touch. While your nose is connected to your mouth. So if you have some problems like coughing or rhinorrhea, both your nose and mouth will have reaction. While if you suffer eye disorder, you may not have some suffering in you nose.