Light sensitivity is unfortunately one of the hard ones to "desensitize" to. You can do things to work on other senses if you have other sensory sensitivities, and being less sensitive in your other senses should help. What other senses do you have issues with? I might be able to give advise there.
If you wear regular glasses, adding things to the sides, to block out peripheral vision can help some people a bunch, and doesn't look too odd. Some glasses have those built in. So you'd want to get those well made if you do that and are trying to make them not look odd.
Reducing visual strain over the course of the day helps. So even if you're not wearing the sunglasses in the grocery store, having ones that are good for your eyes in particular whenever you're outside, and doing things that reduce visual strain in your room helps. Things like changing the sort of lighting you use to lighting that affects you least (I personally like LEDs best, and I like cool white, instead of warm white, but many people like warm white, figure out if you like warm white or cool white, and what sort of bulb works best for you, use that in your room/house). Similar to that, when you're on the computer, do things that reduce the visual strain, if it hurts to look at black on white text, make it white on black. Maybe make it black on green. Do what helps. There are ways to change colors, or tinted overlays that you can put over your computer screen that could help.
If you can make it so that overall its easier, then you can choose when you are able to spend the "I can do something harder visually", and not need to always look weird, if not looking weird is important to you.
I'd say most important is changing the lighting in your house, and figuring out what other senses are bugging you and if there are things you can do to help them.