I too have throat scaring. I hope sharing my experience helps you a bit, OP...
I got mine from an extensive accident at age 15, a rather delicate point of life when it comes to personal looks, let me assure you! First, I'd like to say that yes it does fade a lot eventually. Second, most people genuinely don't mean anything by it, and will often offer their own stories or condolences for your experience. I condensed my story into a one liner and said it often enough it wasn't painful anymore. For anyone who pushed about "what a shame about your looks" (yes they did and yes I thought it hogwash even then) I'd cheerfully mention that they never better see me in a bikini as the damage was fairly extensive. Then excuse myself. ( Happy story, most of it is hidden by baby stretch marks now.)
Out of all the prying strangers, one became exceedingly disgusted, you could see the look on her face change as she realized the scarring was real. She asked me if I could cover with a scarf (no, I was in a work uniform), or makeup (no, the scars were new enough all makeup attempts resulted in pain). I joked I was going to tattoo barbed wire on my throat when I turned 18. She shut her mouth and never came through my grocery line again. I did see her speaking animatedly to a supervisor and gesturing at me, but the supe never said anything to me and I knew the store didn't hire us for our looks so I guess her complaint was found without merit.
I did start wearing a lot more turtlenecks to school though.