There’s nothing to worry about, it’s perfectly natural. There are small openings in the inner corner of your eyelids that allow the drainage of excess fluid, such as eye drops, into a tube called a tear duct (nasolacrimal duct). The eye drops are then transported to the back of your nose and throat and can be tasted. This system usually removes excess tears that lubricate and protect our eyes from infection.
On a side note, this link between the back of our throat and our eyelids also explain how someone can appear to ‘drink’ a liquid, such as milk, and shoot it out through their eyelids.
Chi Wing Man, Science Museum