This may seem strange , but if you have "dry eyes", that your eyes constantly stream.
What happens is that for some reason, the actual make up of your tears has changed. The lipids that are in tears can decrease for many reasons and when this happens, your tears ducts produce extra to try and help keep the surface of your eye lubricated.
You could try the eye drops for dry eyes that you can buy over the counter from Boots etc and see if it helps. You might also find that a hot pack eye mask that you warm and put over your eyes in the evening may make you more comfortable.
I was a Clinical Opthalmic Assistant for 14 years, and this is quite common. Obviously, if none of these help, have a chat with your GP or even an optometrist- there are some still open for emergencies or they may be able to advise over the phone.