Dream never shot at his brother with the intention to seriously wound him, he knew that shooting his arm, leg, tentacles was alright because he would heal, he would have never directly aim for his eye or any risky zone, Nightmare really just moved at the wrong time. And yes Dream dropped his weapon instantly when he saw and heard Nightmare's pain, the scream very much keeps resonating in his head and his nights are plagued with bad dreams.
Yes, people would congratulate him because to them ? Nightmare got defeated, he isn't out causing chaos anymore, the fights are over, he can't harm anyone like that, and he frankly got what he deserved, so people are happy with what Dream did, and Dream is horrified. He never wanted that to happen, seeing people celebrate it and congratulate him truly makes him sick, and he despises each and every one who finds joy in the situation. Dream would isolate himself from the Omega Timeline, he doesn't want to see people celebrating his brother being hurt, doesn't want to play nice to them, so he stays far and practically never visits. He kinda becomes a hermit from that point.
Everyone being convinced he did it on purpose already is bad, but his brother believing that too ? It finishes breaking Dream. And Nightmare truly is convinced it was not an accident, he knows Dream is skilled and never misses his mark, he saw the determined look on his face (the sudden pain and positivity made him miss the horrified look and guilt from Dream), so to him it is obvious Dream planned to do that, to hurt him in such a brutal way.
The gang would indeed be very protective, the will make sure nobody can ever reach Nightmare, especially not Dream, the only ones who are allowed are those who were already established as friends ( Error, Ccino, ... ), but nobody else.
Nightmare not being able to see Dream is terrifying to him, in his mind Dream is dangerous, nothing guarantees him that he's not gonna finish him off now that he's defenseless, and it truly brings him back to Dreamtale and awakens the trauma. His gang had to reassure him many times when he would get paranoid outside, even without Dream around, because any noise would startle him if he didn't know the source.
Dream can both feel and see this terror, and he knows he is the one who causes it. He hates it, and he hates himself.
Nightmare had lived in his castle for many many years, but to suddenly be deprived of his sight after such an accident left him nervous even between the walls, he can't see what is at the corners, doesn't recognize the hallways, ... and all that makes him reluctant to be alone, so at first he would ask for someone to stay with him, just the time he gets used to it. His gang never left his side, and they do their best to make everything feel safe again, make sure Nightmare can feel at ease again when at home.
The closest the twins can come to "peace" is that they are not fighting anymore. But Nightmare is terrified of Dream and Guilt is eating Dream alive. They don't talk, because Nightmare doesn't want to be close to him and Dream wouldn't even know where to begin to apologize in a way Nightmare would believe him.
If they talk again, it won't be before many, many years when Nightmare feels like it and ONLY when he feels like it.