Absolutely no.You can feel free to wear your reading glasses as much as you like. In fact, reading without needed reading glasses will simply strain your eyes and tire them out and your eyes will go even worse than before.What you should notice is to make sure that the reading glasses you choose are suitable for you.
If you get blurry vision when reading or you find difficult focusing on the near objects when you do near task, you may suffer presbyopia. Then you should see an eye doctor and have your eyes checked. If you get presbyopia with different power in both eyes, the doctor will prescrible a pair of reading glasses which are called prescription reading glasses for you. As long as the prescription reading glasses fit you correctly, it can help you see better when reading without damaging your eyes.
If you want to know whether you need a pair of reading glasses, you can see an eye doctor immediately. He or she will have some test for you and then tell you whether you have vision problems or not. If you can't see the letters in a book clearly, and you need to hold it in an arm's distance to view it, you may need to buy a pair of reading glasses.
If you are over 35 years old, and have difficulty to focus on the letters in a book, you may suffer from presbyopia which is a kind of eye disease. and you may need to buy a pair of reading glasses. If you need the reading glasses to help correct your vision problems, your reading glasses will not damage your eyesight on this occasion.