There are several possible reasons. First, the fact that he was shunned by many in the village because of the Nine - Tails is a big factor. Second, his lack of a traditional family upbringing means he lacks that sense of unconditional love. He may have seen other kids with their families and felt left out. Third, his early failures in the ninja academy and being looked down upon by some of his peers also contribute to his feeling of being unloved.
One reason could be his status as a jinchuriki. People might be afraid of him because of the Nine - Tails inside him, so he feels unloved. Another reason is that he was an orphan, and without his parents around, he may have felt like he didn't have that family love that others had.
Well, it has a huge impact. Naruto's sense of being unloved can lead to his over - eagerness to be liked. He might take risks he otherwise wouldn't just to be seen as a hero. And it also affects his self - esteem. He doubts himself at times, thinking that maybe there's a reason people don't love him. But this also drives his growth as he works hard to change people's minds.
His past experiences of being an orphan and often being shunned or bullied as a child might resurface in the fanfiction. These memories can make him feel alone even when he is surrounded by people. He might feel that no one truly understands what he has been through.
One reason could be that the fanfic writer wants to deviate from the original narrative where Naruto gradually gains acceptance. They might want to put him in a situation where he has to struggle more with being unwanted to make the story more interesting. For instance, they could write a scenario where new characters are introduced and they shun Naruto for some reason.
One possible reason could be that he has been through so much trauma that he has numbed himself. For example, all the losses he has endured during his battles and in his personal life might have made him build a wall around his emotions.
In fanfiction, Naruto could feel sick due to overusing his chakra. He often pushes himself to the limit in battles and training, and this excessive chakra use might take a toll on his body, making him feel ill.
His parents' death also contributed to his loneliness. Growing up without them, he didn't have that family support and love that most kids had. He had to fend for himself and deal with his feelings of abandonment all alone. And in the fanfiction, perhaps his friends are too busy with their own missions or problems, leaving him feeling isolated.
One reason could be some sort of special jutsu or power - up. Maybe he got a new form or ability that suppresses pain. For example, it could be related to his Sage Mode or something new entirely.
His fighting style could become more aggressive. Without the fear of pain, he might be willing to use more extreme techniques that would otherwise be too dangerous because of the pain they cause to the user. He could push his body to the limit more often.
Perhaps as a sign of rebellion. If Naruto has some issues with the established norms in his village or with the ninja system in general in the fanfiction, getting piercings could be his way of defying authority and showing that he won't be restricted by the traditional ways.
One possible reason could be a miscommunication between them. Maybe Anko feels neglected and then strays. Another reason might be that the writer wants to create a more complex and angsty plot.