There are several types prescription sports glasses that could possibly meet your needs. They typically seal against the face using a soft material like silicone. Some of them can be ordered as sunglasses, though I don’t know what tint % ranges they provide.
But because of the pressure needed to seal like that, you may not find them comfortable in the long term, and they might even create a mark on your face if you wear them too long.
Be a bit careful of prescription swim goggles and snorkle or dive masks - because water has a different “index of refraction” than air, your prescription needs to change. You could contact those companies to see whether they can fill them in a way that will work in the air.
There are also (land) sports safety glasses that do the same thing. They are meant to protect your eyes from collisions, or fast moving balls, etc. Ski goggles (prescription, or non-prescription that fit over your glasses) are another example.
Maybe motorcycle helmets could work - but in warm weather, your head could get very hot inside, because in the car you don’t have an airstream to cool you off.
In any event, you may also have to use a good anti-fog agent, because the seal reduces ventilation. They vary in effectiveness. For another purpose (ice skating while wearing Covid masks) I had fairly good results from Lenscrafter’s very overpriced spray bottle anti-fog fluid. But not nearly as good as with ZenniOptical anti-fog coated glasses, ordered with extra “activator cloths”.
I’m not as sensitive as you. It’s been decades since my Lasik/PRK surgery, so that’s not the problem. I have often shopped at truck stops. They tend to have many wrap around glasses that might fit over your glasses that you can try, and see whether they fit. Also try dollar stores, like Dollar Tree. They might just happen to have a pair that works, cheap. And try lots of other stores, like department stores, as well as lots of glasses stores.
I’ve actually had pretty good results by simply picking glasses frames that fit me well, and bending them to fit better. I buy sight unseen from from cheap Internet glasses providers like Zenni Optical and EyeBuyDirect. They might or might not seal as well as you want - so maybe try several frames. They are much cheaper than brick and mortar stores, so you can afford to. But there are usually tiny places at the edges where sunlight gets through. And both merchants take about 2 weeks to fill orders from the U.S.
Both of those Internet merchants provide glasses that are every bit as good optically and mechanically, AFAICT, as local stores, even if you buy the cheapest frames. There are other similar Internet merchants I haven’t tried. (Dollar stores provide pseudo-prescription glasses that are pretty good optically too, if you look for unscratched ones - but both eyes in the dollar store ones are identical, they don’t handle astigmatism, and they are mechanically inferior - the screws and threads are junk.)
What I did first was to go into a large glasses store, and look to see what frame sizes fit me best. I also took measurements on the width of my face. Internet suppliers can fit me a lot better than any glasses store I have found, because they have a wider range of sizes. In particular, the only ones in stores that come close for me, because I have a narrow head, are child size or small lady’s size, but I’m a man and don’t prefer child or feminine styles - though if it’s just for inside the car, maybe that wouldn’t matter as much.
You also have to estimate the distance between your eye pupils (IPD=interpupil distance). You can do that in a mirror (using your current glasses if you are farsighted). But most people’s eyes come about 2 mm closer together in close vision (though mine are about 1 mm closer) than far vision. (In fact, when I told Zenni-Optical that I wanted my close prescription with only 1 mm smaller IPD than my far prescription, they called me from China to find out if I had made a mistake. Pretty good service for very inexpensive glasses.) BTW, some people have asymmetric faces, so you may have to measure left and right distances from the center of your nose.
There ought to be a type of removable sun shade you could put over your windshield. Maybe you could make one that rolls down from on top to cover the as much of the windshield as you need. Or a big adjustable position piece of cardboard you somehow mount on your sun visors. Or airplane style, where you can position an opaque shade anywhere the sun is. All are probably illegal in cars where I live (Maryland), because in theory you can’t legally block any part of your windshield, not even with a GPS or enlarged rear view mirror or parking sticker, or cell phone (many people do it anyway), but that might not be true in NY. (Do I recall that NY inspection stickers actually go on the windshield?)