Hi Ethan
I am so sorry to hear that, it does look worrying actually.
I have heard/read somewhere, that fishes can get stuff "stuck" in their gills, like small rocks and snailhouses...And that sometimes corals can even try to grow in gills, or featherworms... and as such I hoped to tell you that it might just be something stuck in its chin, but with the added picture of the whitish gill-edge, I cannot really be sure about what is going on with the little fellow.
I just got a clownfish that had something stuck in its gill. I saw it in a store two years ago with this "something in gill", and as it was still there this month, still with this growth just sitting there, I bought it and fixed it in under 24hrs.
It was slightly coneshaped, seemed similar to the shape on your picture but more darkish grey. I tried running a nail over it, but it seemed completely stuck.
If you know what tool I mean, I then used a cuticle knife, the ones with a small v-shaped blade, carefully running it with the gill and upwards to let the v-blade catch the growth ....and the substance slit right out of the gill.
I had feared that, if this was a parasite, it would only make it worse to tamper with it or try to remove it but it was not the blade actually cutting it, just the right direction for it to slide out, adding to the possibility that it was simply something stuck. I examined the greyish stuff and it just looked like some rocky crystalline growth, and after it dried out, it collapsed further into what I would describe as some random aqua-debris.
So, I am but a novice aquarian, I don't know anything that can help you, and I share your worry that your fish might have something worse going on than what I removed, but hopefully you'll get it cured in no time anyway & make sure that it is not just something stuck in there
It is such a peaceful hobby, yay!