Hi. I'm online and happy to answer your question today.
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You are likely experiencing a PVD or posterior vitreous detachment, a common event that happens in many people. You have a thick gel material in the middle of your eyes. Over time as it liquefies, this gel material collapses on itself and pulls away from the wall of the eye. In the process it can stimulate the retina -- causing the flashes that you see. It is recommended that you see your ophthalmologist to look at the retina to make sure there are no problems such as a retinal hole or tear. In most cases, there are no problems, but this exam is precautionary and allows for preventative treatment of any lesions that are found. If you notice a sudden increase in floaters, flashes of light (like a lightning storm), or a shadow/veil in the periphery of your vision, this can be worrisome for a retinal detachment. You would need to contact your ophthalmologist promptly in that case.
I agree with the urgent care MD -- you should be ok until Monday. A visit to the emergency room, unless you could be evaluated by an ophthalmologist, would be of very little value.
I am concerned because it does seem to be like a shadow or veil that is on the left side of my right eye. If it is a retina detachment, is there anything I should avoid doing until I see a doctor? Can a retina detach for seemingly no reason?