Timeline

Source: https://inuyasha.fandom.com/wiki/Kagome_Higurashi#Inuyasha

Beginning:
When Inuyasha thought Kikyō had betrayed him, he was initially hurt and angry and took it out on Kagome thinking she was Kikyō as they both look similar. Inuyasha eventually realized that Kagome wasn't Kikyō and slowly opened his heart as she showed him kindness and compassion. She attemped to be his friend and eventually more once she discovered his more gentle side and similar mindsight of life. However, their friendship and eventual blossoming romance, does not stop Kagome from shouting "Sit!", (sometimes "Sit boy!" in the English dub) either to keep him from misbehaving, to childishly get her way, by accident, or when Inuyasha hurts her feelings in some way. Overall, throughout the series it is shown from the beginning to the end that they have come a long way from being close friends to falling strongly in love to the point where they become fiercely protective of each other, Her wild, turbulent emotions towards Inuyasha can range from concern over him to relief at seeing him safe to anger over his reckless behavior despite the fact that she shares this trait, and then burst out sobbing her mixed emotions. In Fateful Night in Togenkyo Part II, where Inuyasha was willing to shield himself in order to protect Kagome from getting hurt and when Kagome fearlessly threaten Tōkajin that if Inuyasha is hurt then he would be sorry, despite being incredibly shrunken at the time.

Part One:
Their relationship is seen and discussed at length by Sango and Miroku, who talk to Inuyasha and Kagome on their respective gender sides (Sango talks to Kagome and Miroku talks to Inuyasha). Shippō also shows immense dedication to their relationship, and despite his friendly arguments with Inuyasha on the matter, encourages him to go after Kagome, if only so that she returns to all of them. This shows that it appears that everyone is aware of their strong romantic feelings for each other, from Kagome's modern-day friends and family to even their own enemies such as Naraku.

Part Two:
However, their relationship sometimes becomes strained and complicated due to Kikyō. Whenever Kikyō becomes involved somehow, Inuyasha drops everything around him so that he may protect her, events to which always lead to Kagome's feelings becoming deeply hurt out of impulsive jealously, even though she knows its mostly out of guilt. Initially, Kikyō had also been the source of many of Kagome and Inuyasha's fights, to the point sometimes Kagome even had considered leaving Inuyasha despite she is in love with him, as it was too difficult for her to be with him knowing he still harbored feelings towards Kikyō. Kagome, however, has always been able to somehow learn to look past these doubts and always comes back to Inuyasha's side and their love for each other only keeps growing stronger and stronger.

Part Three:
Aside from Kikyō, there have been other obstacles in their relationship, such as Kōga. When they first met Kōga, he kidnapped Kagome as she has the power of sensing the jewel shards. However, he eventually develops feelings for her and claims her as "his women" and thus he also becomes Inuyasha's rival, whenever the group runs into Kōga, he and Inuyasha always get into fights, mainly about Kagome. They get into fights over protecting Kagome or wanting to gain her attention and affection, Inuyasha has never felt easy whenever Kōga is near as he believes that Kagome might actually harbor feelings for him. Kagome, however, doesn't have feelings towards Kōga always kindly rejects his feelings. Though Kōga knows full well that Inuyasha is in love with Kagome, he is oblivious to the fact that Kagome is in love with Inuyasha and does not return his feelings. During Vanished in a River of Flames, that is when Kōga finally understands Kagome's incredibly strong feelings for Inuyasha, becoming surprised when he saw how worried Kagome was for Inuyasha after the explosion and also saw how happy and relieved she was when she saw that Inuyasha was alive and alright. Despite knowing that, Kōga stated that he would never give up on trying to win Kagome for himself.

Part Four:
Overall, despite the arguments and obstacles in their relationship, ranging from overbearing jealously and impulse to just pure childish stubbornness on both parts, Inuyasha and Kagome's feelings for one another are strong and pure as it shows they both care a great deal for each other. The bond the two of them share also shows that they would go to great lengths to protect each other or help in any way they can as they could not bare seeing the other so devastated, hurt or unhappy to the point of tears, especially since Kagome is the first person Inuyasha has ever shed tears for. As time goes on, Inuyasha and Kagome are shown to learn to overcome anything either it being arguments or rivals and are shown to becoming more closer to each other than ever before. This shows that the two of them are able to overcome just about anything and along the way, the stronger their love becomes.

Part Five:
During "InuYasha: The Final Act," it is a big step in Inuyasha and Kagome's relationship. At the start of the series, their relationship is still the same from where the show left off with Inuyasha in love with Kagome, but yet at the same time he is still in love with Kikyō. However, after Kikyō died for the final time, just when Kagome finally made peace with her jealousy for her, Inuyasha was finally able to move and finally, but slowly realized that Kagome is and always has been his one and only true love. The two even almost shared a kiss with each other but were interrupted by the sudden arrival of Kagome's family. During the final battle within the Shikon Jewel, Inuyasha finally realized that he and Kagome were destined for each other as he claims Kagome was born for him and himself for her.

End:
Eventually once Inuyasha and Kagome were finally reunited within the Jewel the two of them finally shared the long-awaited kiss with each other. With Inuyasha by her side, Kagome wished away the Shikon Jewel's existence forever. Due to this, the Bone Eater's well stopped working and they were separated for three years. Soon, Kagome is eighteen years old and was able to return to the feudal era as it was thanks to her strong desire to see Inuyasha again that the well finally connected once again. After returning and being reunited together, Kagome and Inuyasha soon got married, which is revealed to readers and viewers of the manga and anime when she calls out to Sesshōmaru as Big Brother (お兄さん). Now, Kagome is adapting to her new, permanent life in the Feudal Era as Inuyasha's beloved wife.