No, you don't need a prescription for it. They sell it at the drug store although here it doesn't seem to be as prevalent as dramamine. I ordered it either through drugstore.com or
amazon, can't recall (probably amazon).
I have the same thing, I don't actually produce tears at all and what I do is non-nutritive. I have Rx drops for 2x a day and then a couple of different kind of drops to provide immediate relief though I find that doesn't last long so don't really use them much though I probably should.
For me I find that wind causes tremendous issues, as does driving at night or in the rain, basically anything that causes my eyes to strain at all. I do wear Rx sunglasses which helps as I'm not straining to see and have extra large lenses to keep as much air out as possible. Too vain to go to goggles.
I don't know if you've ever tried a sleep mask at night but it can really help them to recover since it blocks the air out whereas when we sleep we don't close our lids 100%, as can a cold or warm compress for more immediate relief. I always joke that I look like Doris Day with the eye mask but it really does help, especially at certain times of the year. In bright sun like that I do tend to double dip these days with a hat and glasses and that aids a little as well. Flying kills my eyes, they usually take a couple of days to recover, they get very dried out in the cabin.
I feel your pain, literally! NO fun at all. For me it's become more a matter of how bad do they hurt, it is rare that they don't hurt at all.
Have you considered the plugs or looked into tear duct surgery? I'm apparently not a candidate but they have the dissolvable ones and then the more permanent ones and we have chatted about trying them just to see if they'd help, though my doc thinks they most likely won't given that the few tears I do make are non-nutritive.