I think this more likely a Visual Looming Syndrome, than Aichmophobia. They are two different things. VLS can be treated with eye muscle exercises. https://en.wikipedia.org/wiki/Visual_looming_syndrome
The only reason I can refer to for the explanation of your problem is psychology. Physically, hurt in eyes may be aroused by external stimulation, inflammation or eye disease. Obviously, looking at sharp objects is none of these reasons. Thus, I think you hurt is inclined to be physiological. Maybe you have been hurt by sharp object in the past, so that you fear about those kinds of things. According to my knowledge, sometimes this kind of problem will disappear with the time flies and sometimes you shall go to see a consultant. Sometimes people take pain killers to release the problem, but it could no cure the problem essentially. The best treatment is to find out your mental obstruction and solve it.
You must have full of imagination. If the sharp objects didn't touch you, it won't cause your any actually damages. Of course, if the shape objects touch you, you must be hurt. So, for your situation, The eyes hurts must be caused psychologically. So, just take it easy. If your eyes really hurt, you'd better to see a doctor.
Because the shape objects stimulate your eye nerves, your eyes may feel hurt. You should avoid such shape objects. But it can't get rid of the condition that your eyes may get dry and get infection which may cause the eyes feel pain. I suggest you to have a check on the eyes fully.