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.
He might focus on his training. By pouring his energy into getting stronger, he can distract himself from his lonely feelings. Naruto has always been determined, and training gives him a sense of purpose.
Maybe it's some kind of special jutsu or a curse that backfires in a way that numbs his pain receptors. For example, a powerful sealing technique might have been placed on him accidentally or on purpose that has this side - effect.
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.
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.
In many fanfictions, Naruto might start by training harder. He throws himself into his ninja training as a way to distract himself from the loneliness. It gives him a sense of purpose and also helps him become stronger.
It might also be about how Naruto is treated or perceived in the fanfiction. If the other characters see him as a monster, either out of fear of his power or because of some misinformation or plot device, then that would create the feeling. This could lead to interesting storylines where Naruto has to deal with being ostracized or hunted because of this false perception of him being a monster.
The plot could involve Minato being brought back to life or having a vision where he steps into Naruto's shoes. He might feel Naruto's pain from constantly being underestimated because of his status as a Jinchuriki. This could lead to Minato trying to find ways to comfort Naruto from afar, or even influencing the events around Naruto in a supernatural way.
One possible scenario in this fanfiction could be that Naruto's friends all got caught up in some mission on his birthday. He's waiting for them to return, but as the day goes on, he starts to feel that familiar loneliness. He then decides to go to the training ground alone and train, using the physical exertion to mask his disappointment.
Sakura would probably be the first to jump into action. As a medical ninja, she would immediately start examining Naruto to figure out what's wrong. She might be worried but also determined to find a cure.