Well, as far as I know, your problems don't seem to be that serious because they are just common symptoms from catching a cold I suppose. Generally speaking,catching a cold could lead to such symptoms like watery eyes and burning eyes. Speaking of how to treat it, I advise that you get some pills and drink plenty of hot water. Do not rely on eye drops, maybe a few days later you will be recovered.
Yes, it is possible for you get watery and burning eyes from a cold. When you get cold, your immune system of the whole body will be weak. Your eye pressure and eye nerves will be affected too. Your eyes may feel uncomfortable and dry which may easily cause the watery and burning eyes. You could use the eye drops to release the symptom. But you should treat the cold first.