Generally speaking, it is dangerous to have this situation. First, because of the flash burn from welding, your eyes will feel flash burning, and at the same time, painful. In some cases, red, bloodshot eyes can occur too. For the treatments, cold compresses are needed. For example, you can just try to use some ice under your eyes, to cool it. Also, you can use a thorough rinsing with cold water, so that it will not irritate the eyes. In common, it will take two days for this feeling to disappear. By the way, you can use eye drops, which are a very good idea.
When you gets hurt in the eyes during the flash burn welding, you could find that you have great burn on your eyes. You will feel that your eyes will not be able to open. What's worse, you could find that you can't help watering at the eyes. Your eyes will be afraid of the eyes. However, after the 24 hours' rest and treatment with the medical treatment, your eyes will get recovery.
Ok, it seems that you worry much about your eyes and are afraid of getting burned by those welding flashes. Actually, those flashes are quite terrible and damaging to your eyes, which could lead to constant watery eyes, blurry vision, extremely painful eyes, photophobia, even blindness, and maybe some infections. In a word, that is very dangerous and you should be careful not to get those in your eyes.