This might sound like an odd question. I'm using prescription eyedrops at the moment and each time I use them, I get a really nasty taste in my mouth. Is it possible that they are making their way internally from my eyes to my mouth? As you can gather, I'm not great at physiology.
Have you ever seen Kevin and Perry go large? There is a character in it who drinks alcohol through his eyeball and gets wrecked so yeah I reckon there is a connection there somewhere. ie when you cry why does your nose run?!
I was very tired the other night & accidentally squeezed two drops of my nose spray in both eyes, instead of my eye drops. I waited for something terrible to happen, but it didn't! I wouldn't think that eye drops trickling down to your mouth would do much harm.
One of the noted side effects of the commonly used eye drop preparation Chloramphenicol (used for conjunctivitis and other minor eye infections) is a metallic taste in the mouth. The mechanism by which this is caused is poorly understood.
The tear ducts do drain into the nasal passages, and this then drains into the back of the throat.
When you're putting your drops in, make sure you cover the drainage point in the eye. On your lower lid, there's a pin prick hole in the inner corner of each eye - press down on that before you put your drops in and keep it depressed for about 20 seconds after. This will minimise the amount of the drug that is systemically absorbed and runs down into your nose.