It's a quite normal phenomenon while rubbing your eyes. The most possible reason is your eyes probably get infected, because there is some dust or eyelashes in your eyes. First of all, stop rubbing your eyes. Then check out whether there are something in your eyes, and you can do this on your own with a mirror. Next, let the foreign matters out of your eyes if there is, then you will be fine. If there's nothing in your eyes or burning is still exist, use some teardrops to relieve the feeling or put a tea bag on your eyes. All in all, no matter what is the reason, do not rub your eyes. Because rubbing the eyes too hard will give your eyes a heavy strain, which can break capillaries and make blood clots form, or even give rise to to detached retina.
Well, from what you said, I can see you have got some problems with your eyes. As you know, itchy eyes could be a sign of health problems, such as red eyes ,pink eyes, fatigue or eye strain. If you keep rubbing your eyes with dirty hands, you are likely to get infectious eyes and suffer great consequences. I suggest that you try to get some anti-biotic eyes drops to treat the problem. And give up some bad habits and make good use of your eyes.
It is easy for you to get invisible bacterium when you rub the eyes. You will easily get red at the eyes. If you rub the eyes too much, your eyes will easily feel itches. You could use the eye drops with anti-inflammation to release it. In addition, the warm compress is also a good way for you to make the eyes get comfortable and moisture.