Yes, it really exists such sensitive character. Your nose pad must be changed through many year's sweat and so on. You'd better change new eyeglasses. And you should keep in mind that you will tell the eyeglasses store that your nose part is sensitive. Thus, he may take care of this and help you choose one that will not irritate your nose.
In fact, i don't believe that it will get nose irritation from nose pads. I once have a pair of metal eyeglasses that wearing for 7 years. And i still remember that i worn the eyeglasses with yellow and green nose pads inside. And i am still in fine and never suffer any nose irritation. So, you needn't worry that. Nevertheless, to be good to your eyes, you'd better get an eye check to see if your vision changed and need new eyeglasses. Usually, people's eyesight will change every year.