I think you can definitely learn to not be as affected by these sounds as you are right now.
I think part of it comes down to practice.
I’ve never been as sensitive to sound as you (or others above me) have described, and so I don’t necessarily know the most effective exercises to help with that. But I have noticed, just on my own, that my ability to ignore certain sounds wanes without practice, and strengthens with practice, so I think it’s a skill that people can develop.
If you are close to panic attacks with these sounds, it might be worth investigating cognitive behavioral therapy (CBT) or a similar kind of approach. I don’t know it in great detail. I do know of a YouTuber that describes her own experiences with it (in an ongoing series). Not sure where she’s going with it, or if it would help you, and she’s very clear to state that she’s in no way a doctor or professional—she’s just relaying the specific strategies she was taught, the way she understood them. Might be useful for you, so I thought I’d share: Part 2: CB Model
When I find a sound annoying me, personally, I try to pay attention to it and figure out what about it is bothering me. Once I’ve located that, I try to mentally “let go,” of either the frustration or the attention I’m giving the sound. I remind myself that it’s just a sound, it’s just sound waves passing by me that my ears happen to notice, and I don’t have to pay it any more attention than that. I’m by no measure very “good” at meditation, but I try to think of it in that kind of frame, of noticing what I’m feeling and sensing, and then just letting it be, letting it go.
I guess I’m fortunate in that I’m pretty good at mentally ignoring noise I don’t want to pay attention to. As far as it’s a skill, I think I developed it at least in part from eavesdropping in crowded/noisy places, like a coffee shop. I like to hop from conversation to conversation, so I practice keying in on certain sounds while letting everything else fade into the background. And then I switch when I get bored, searching for another conversation. I think that habit of mine has allowed me to learn how to “let go” of sounds to be able to focus on the ones that matter.
You might try doing that too, either by seeking out noisy places and eavesdropping, or by, when you’re in the classroom, trying to focus on just one of the sounds (to keep your brain from going to all of them at once). Notice that specific sound, focus on it for a time, and then imagine letting it go. Focus on another single sound—not letting the other sounds pull your attention. Then imagine letting that one go. Etc. Again, I’m not sure if that’s something that would help you, but it’s something like what I do, and that works for me.
I’m also not saying it’ll be easy or immediate, especially if these sounds have become stressors for you—it’ll take time to disassociate them from that stress. It’s not always easy for me. It does take some effort.