I don't know how long ago this occurred. If you flushed the eye immediately, and there is no pain or decrease in vision, then you can use artificial tears for comfort until the burning improves. Also, STOP smoking!
As Dr. Fazio states, for the sake of your eyesight it is critical that you stop smoking, but not because of the danger from cigarette ash.
There are a LOT of patients on these boards who would be glad to have their eyesight back, but can't do anything about it. In your case, you don't already have eye disease. Smoking cigarettes can harm your vision in many ways. In case you are not familiar with these, please read the following:
Many users here would gladly trade places with you because they already have cataracts, macular degeneration, uveitis, retinal bleeding from diabetic retinopathy (smoking doubles the risk of diabetes). Lots of people develop these diseases even though they do not smoke. There is often no reason why these problems arise in patients and severely affect their eyesight.
The fact that you could stop smoking and reduce your risk for all of these complications gives you an excellent reason to quit. Please try, for the sake of your vision and for those who depend on you.
There was a big fire in Canada at a nursing home recently. Any smokers involved?????
Add this to your reasons to quit.