Hangnails: What's the best way to deal with them?

I’ve run into a real nightmare here. I have this cluster of what looks like raw, inflamed tissue—granulation tissue, I think the doctors call it—growing right out from an ingrown toenail on my right big toe. It’s honestly revolting. I’m wondering if there’s any way to deal with this without going under the knife again. Back when I was in Chicago about two years ago, a plastic surgeon had to excise a quarter of the nail on my other foot to fix the exact same issue, and frankly, I’d rather avoid another procedure if possible. Right now, I’ve been using some antiseptic soak to try and draw out the infection; it helps the swelling subside a bit, but that angry little growth just won't fully retreat 🙂
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Look, I can easily reach the nail and trim it myself, but the whole mess remains—it still feels like the nail is digging in, leaving this hideous irritation behind. Does anyone know of any other way out of this? Is there a specific ointment, a specialized treatment, or anything at all... just something to get rid of this disaster so I can finally wear sneakers without constant pain 🤷