Those glasses probably won't do much good if the wavelengths reported are accurate, but if the wavelength's are closer to the near-IR range or maybe mid-IR, then glasses could help. Near Infrared (IR) is closer to the visible spectrum, 700-1,400 nanometers (nm). Mid is longer and Far is even longer. There's no one clear guideline where near IR ends or where far begins, but IR sauna's in general operate between 3,000 and 14,000 nm wavelengths of light. Source and Source. If your Sauna is in that range, the glasses won't do much good, as IR glasses mostly block near IR light in the 700 to 1,400 nm range, occasionally up to 2,000. (available through various sources, usually listed in the fine print where glasses are sold).
IR light, mostly near-IR light can be bad for your eyes because your eyes don't recognize it so the pupils don't contract. A simple solution if it's dark inside the IR Sauna would be to bring a light or flashlight inside with you, reflect the flashlight off a wall into your eyes and your pupils won't be fully dilated. Not so bright that it's uncomfortable, just bright enough that it's not dark. That might work as well as, maybe better than glasses. But If the Sauna is closer to near IR than far IR, then glasses could help. One way to test that would be to feel for hot spots along the wall and stick a thermometer into the paneling to see how high the thermometer gets. Many less hot heaters means far IR. Fewer hot spots means mid-IR. I wouldn't think a heater would generate much in the near-IR range unless it was very hot, like Oven/broiler temperature.
IR light mostly isn't dangerous, it's basically just heat so you should be able to feel it when there's too much of it. It can be moderately dangerous if there's enough of it because your eyes don't contract in it's presence. A sauna shouldn't generate high exposure cause if it did, it would cook you like a roast, but long term low exposure has a chance of being hard on the eyes.
As a general rule, anything that will block light in the 3,000 to 14,000 nm range will need to be a conductor. Aluminum foil will work, but you can't see through it, however you could do an experiment and see if blocking your eyes with aluminum foil or aluminum foil wrapped around a towel does help. Some types of films or oxides like
It's worth considering that it might not be the IR light at all. It could be the heat or the dry air or even some chemicals or formaldehyde from the paneling (check for made in China) or mold or cleaning supplies that get suspended in the air in higher temperatures or even sweat and skin cream you use that might drip into your eyes in the higher temperature. If I've completely freaked you out, then I apologize, but all things should be considered. Far IR light is mostly harmless, so it could be something else.