No, you definitely should NOT make a separate class for each button!
A class is a type of thing. You should only make multiple classes if you need to have different TYPES of buttons (For example if you need an ImageButton that displays an image that you can click on and a TextButton that displays text you can click on, and a ToggleButton that you can click once to push it down and click again to pop it back up).
If you just need multiple buttons of the same type (but different text, different positions, etc), then you should just have ONE Button class, and then multiple *INSTANCES (objects) of that class.
It sounds like there's another bug going on in your code that's preventing the buttons from displaying -- have you checked:
1) are all the buttons in the same place, being drawn on top of each other?
2) are some of the buttons being drawn outside of the window boundaries (coordinates too big/small?)
Feel free to post more of your code here. Since no one is doing the same nifty project as you, there isn't any concern about people copying your code. (And if someone does want to use your Button class code, they are welcome to do so AS LONG AS THEY GIVE YOU CREDIT in the "Assistance" section in the top comment header!)