I have dry eyes and skin problems around the eyes but a lot of saliva. We thought of that though. I did recently try some Visine and I have used it before but this time it set my eyes on fire like I had poured rubbing alcohol in them. I haven't tried that again..
Still catching up on this thread, but wanted to let you know I have the exact same experience with the eyes. I also have a few crossover symptoms I share with your situation, but I won't get into in this post.
I used to use Visine of all types (natural tears, etc), and now can't take eyedrops without intense stinging pain. Eye doctor said my face and cheeks/eyes were inflammed. Diagnosed with eczema tentatively but dermatologist was baffled due to the presentation (resembles more Lupus, but atypical set of derma symptoms with sensation changes in the arms/skin/heat/friction sensitivity is often accused of being Lupus, and its my personal suspicion that any doctor that rushes to a Lupus conclusion is a little suspect). I found myself leaning towards Lupus too often too, and setting that aside helped me work it up from another angle.
IGE out of range by 40 points (significant, as IGE is involved in the heavy duty inflammatory actions that can be quite destructive if there is a problem-- dismissed or as you say, "yawned" at), ANA weakly positive at onset (never rechecked). Ran through the system lost with "you're fine because you're a white male" doctors, so I burned out of the process ultimately being left with no definitive answer. I even blew off my inflammatory marker bloodwork 2x because I just didn't care anymore. I was beat.
My GP and derma initially denied the symptoms, despite my eye doctor writing my face and eyes had inflammation. And despite me explaining that my skin was so incredibly dry, that it required at least 1 daily application of heavy duty moisturizer on the face and arms. Even prescribed SSRI's (of course! getting high as a kite is the solution to everything) The dermatologist backed up the GP and pushed the SSRI's (going against the eye doctor who originally declared there was clinical inflammation in the face/eyes) it wasn't until I started working with more doctors I started figuring it out over the course of 2-3 years and I still don't have it all figured out-- as there is only so much you can do.
I saw a neurologist as well for headaches that began and lightheadedness around this same time.
It was exhaustive, eye opening, and you tend to lose faith in the medical system when trying to work up a "quality of life" problem (despite physical symptoms). Thankfully the symptoms abated mostly after a full year, and I've mostly chalked it up to allergic eczema but that's kind of just a cop out. I'll start the process up again maybe some day. I learned a lot, and I guess I have to see the positives in it overall. I read so many medical books and journals for about a year and gained a lot of understanding on various biology and processes.
Also, numbing drops for eye test at the doctor REALLY fucking hurt for 3-4 hours (they already hurt before going to the doc) . I refuse drops and tests that involve them to this day, mostly out of principle, since they brushed off my symptoms, never offered a Restasis trial to see if dryness/inflammation was out of control, and passed me off to a newby doc because I DARED to come back a second time for the same symptoms and offended the doctor by declining any painful examination (eye drops). Antihistamine drops were worthless, as were lubricant drops.