If you got itchy feeling at the corner of eyes, it might be eye dryness or infections. If I were you, I would prefer to wash the eyes immediately. On one hand, it could wash the bacteria or virus out of eyes. On the other hand, it could also moisturize the eyes. Apply some warm compress on eyes and have more water which are very helpful. Actually people always feel itchy eye when eyes are dry. Drinking more water is the easiest way to ensure enough water supply. Have light diet and fresh fruits and vegetable because vitamins are good and essential to eye health. Omega-3 fatty acid could relieve the dryness too so salmon fish is a good food resource.
Itchy on the corner of your eyes is possible to be caused by infection, injury to eyes, allergies and eye discharge. Before you get the certain reasons, you can apply hot washcloth to wipe the corner of eyes with different places of your washcloth. If your condition is still the same try to drop some basic eye drops to relieve your pain and itchy. Well, observe your condition for 10 minutes, if your severe condition still exists and I think it is time to hold consultant with an oculist as soon as possible.
Well, for your situation, I have to say that your eyes may be infected by some stuff. So you need to be careful about it. Generally speaking, when your eyes are infected by some bacteria, allergies, there will be some symptoms occurring in your eyes. For example, your eyes will be red, watery, dry, sore, burning. And of course, itchy eyes can be possible too. At this moment, you need to try some ways to find the real reasons. And also, having some cold compresses with ice can be very good for your itchy eyes. By the way, you can just wear a pair of eye patch to protect your eyes from further infection.