Mucous membranes (think of skin like the inside of your lip) readily absorb most medications. Your eyes, nose, mouth, etc are lined in mucous membranes. They are contiguous; the eyes drain into the nasal passageways, the nasal and oral passageways are united at the nasopharyx.
Basically any over the counter or prescription nasal sprays or eye drops that you would use at the recommended dosage, if they dripped down your throat, would not be toxic in the mouth/stomach any more than in the eye or nose. Even if they taste gross. HOWEVER, this is only true at the doses you should be using them, for the small amount that might drip down the back of your throat after proper application.
This eye drop, for example, can cause toxic effects in kids at 1 or 2 ml dose. But that's much more than the few drops you should be administering. This is an article on child poisonings from drinking eyedrops.
Think of how Visine helps constrict the blood vessels in your eyes to reduce redness. So you use a drop or two and it acts on the eye, barely anything is absorbed into the blood, and barely anything makes its way down into your nose/mouth. But if you drank a squirt of it, it could have that vasoconstrictive effect throughout your whole body.
So keep your Visine out of tiny hands.
Also, I can't speak for all the special eyedrops used by ophthalmologists, but we're talking about meds you'd use at home.
Some important things to note:
If a nasal spray (like fluticasone or azelastine) is coming down the back of your throat enough to really taste it, you need to make sure you're using it correctly. Look at youtube for videos on how to properly use nasal sprays.
You mention ear drops - that's definitely not the same situation, as your middle ear communicates with your sinuses via the Eustachian tubes BUT your external ear canal is NOT connected with anything internal - it's a dead end. Or it should be. If you have ear drops draining into your sinuses/mouth, go to the ER or an ENT (otorhinolaryngologist) immediately to check for ear drum perforation!
If enough of a topical corticosteroid (e.g. fluticasone) is swallowed regularly, it can predispose to oral/esophageal thrush in some individuals, similar to inhaled corticosteroids. Another reason to make sure you're spraying it right!