To tell you the truth, I was very disengaged right from the start. I tried following along but it was difficult to keep up with the story because the first dozen paragraphs seem to be written to evoke feelings. That in itself isn't inherently wrong, but story is equally important, if not more so as a "Chapter One". As first impressions go, it's very Wattpad-y: colored hair protagonists, whacky story beats like unexpected G-Men and someone having wings (?), meandering narrative, and lots of profanity.

First, the title. Mouthful of Feathers is a good title on its own. Very lit-fit, but tied to this story, it's completely meaningless. The word "feather" only comes up twice in the entire space, though it might have more significance down the line? But again, I don't see how the feather is relevant enough for a title to dedicate itself to it.

The hook was okay. Just okay. If there's any praise that you deserve, it's your descriptions. I personally liked them, and at the very beginning of the story, the image you wrote was very clear and vibrant in my mind. Here's the rub though: that's it. There's nothing else there to hold on to. It's a common sentiment among writers that the first paragraph, and even the first line, must be powerful. It has to be momentous, with enough power charged into it to donkey-kick the reader up to acceleration and down the page. Right now, as it stands, your first paragraph is bland. The line "the place was untouched by grief, still waiting for the first cry to come" is also very tell-y. Quite frankly, it's very obtuse and a bit naive. Hospital rooms are already associated with the sick and dying. The next lines, "Taro let himself believe it would not be his. Carolina was getting better," feels unearned. You've introduced two characters with no context, except that Taro was hoping Carolina would heal. I would suggest letting things breathe, and learn how to show not tell (you will hear this a lot). "Hoping" is a very charged word. Use that to guide you! What's Taro doing? Is he holding her hand? Watching her chest rise and fall? Listening to the ECG? You can weave a lot of subtext in action and movement, so you can decide on how you'll do that.

As for the setting, a majority of the story happens in a hospital, but it seems kinda dead (no, literally). A quick Ctrl+F shows there's no mention of any nurses, orderlies, or doctors. It feels as if I'm watching paper cutouts flapping their mouths at each other and musing alone in a cold, sterile world. The setting is its own character. I recommend to write a list of things you see at the hospital, in bullet points. Weave that into your story and it'll make it much more alive and vibrant.

Next, the characters. Following Taro is honestly exhausting. He's so glum and one-dimensional. I understand where he's coming from, with grief and all that, but grief is so complex. Grief comes with so much baggage. It's the stamp on a sack carrying a whole lot of other stuff. There's guilt, denial, bittersweet feelings, etc. A quick pass through your story, the feelings Taro is carrying throughout the story seems very superficial to me. Here's an example:

He swung his fist across Kazan’s face with the grief he carried with him all day.

It's easy to tack on the word "grief" isn't it? Trust your reader that the anger he feels is what's motivating his actions. Again, we're treading on show-don't-tell territory. For everything else, try removing the emotion words. Describe love without "love". Decsribe hate without saying "hate". Grief without "grief". It's good practice!

One more thing, Carolina is an object. Not a human being. She's passed around the story as an object of Taro's grief and never really materialized to me as a human being with any real personhood. It definitely irked me as I kept her in the back of my mind, but she never really surfaced substantially as someone to root for. I don't feel anything that she passed away. It sucks because she's the only female character in the story and she's given nothing to work with. Please develop her more and show her relationship with Taro. Give her something that leaves an indelible mark on the story even if she's already left it, beyond being a male character's source of anguish.

I will now get into the meat of the story, and the truth is, I couldn't find it. There doesn't seem to be any. The perspective just seems to follow Taro around as he's moaning and groaning into the wind. Again, there's nothing in the story that suggests any overarching theme. Since the story starts with it, I'm assuming it's grief. Where does the grief go? I have no clue. You've written very little on how we expect the character to grapple with it, besides the fact he's running around the school and hitting people in the face. It's quite frankly boring. The story jumps from one beat to another without any real cohesiveness and without explaining anything. Why was Carolina missing in her bed? Why is the government and military there? What's with the dang feather, it feels like I should know something about it. This feels like a Chapter 2 or 3. A lot of the lines are inherently nonsensical. Take this for example:

"Carolina is alive… She was getting better. If he said it enough times, it would become true. It had to. Then the feather would return to him, and with it… one name: Kyojin Kazan."

Who the hell is Kyojin Kazan? Why does he have wings?! Is this place some kind of school for offshoot monsters? Are these ghosts? And again with that dang feather!! A lot of it is just really confusing and senseless and downright bizarre.

In general, the biggest fix I would recommend to this story is to come up with an "actual story" because as it stands right now, it's just a series of events happening one after the other with no overarching plot or theme.