No.
InuYasha was in love with Kikyo 50 yrs ago but due to Naraku's interference, Kikyo died while InuYasha was sealed to the Tree of Ages (or Sacred Tree). All in All Inuyasha is also in love with Kagome who is Kikyo's reincarnation. But In my opinion Inuyasha loves Kagome more then Kikyo (considering that's who he ends up with in InuYasha: The Final Act).
It is the second movie it is a little while before inuyasha and kagome kiss.
In the manga, it shows Sango and Miroku has having two twins girls and an infant son while Kagome and Inuyasha say they're just living with each other. At the very end, Kagome calls Sesshomaru "brother-in-law," so it's assumed Inuyasha and Kagome are married, but nothing substantial about their future is revealed.
In episode 160, Inuyasha lands on Kagome's bike, (which she spends about an hour polishing) she gets mad, runs to school while Inuyasha tries to fix, but ruins it more and more, Kagome had invited her friends to her house, they notice Kagome's bike and thinks its a type of art sculpture. (Inuyasha is sooo dead ^u^)
episode 99. While Koga and InuYasha fight over chips ^_^
Inuyasha takes Kagome to her high school entrance exam in Episode 26, titled "Tsubaki's Curse." In this episode, Kagome deals with the pressures of her exams while also navigating her dual life between the modern world and the Sengoku period. Inuyasha's presence adds both comedic and heartfelt moments as he struggles to understand her world.
In the beginning of the story, InuYasha thought Kagome was Kikyo, so he treated her like she betrayed him like Kikyo did. For a while, he is comparing her to Kikyo, so he saw Kagome as not as strong or powerful, so he treated her poorly. Later he starts to like Kagome, so he gives her more respect, care, and safety. He even becomes overprotective of her when he falls in love with her.
When she leaves after the river encounter. He follows her scent into the well and hops in, and walks into her house unnanounced while Kagome and her family were about to eat Oden.
Actually, it happened in the 2nd movie, not an episode. Inuyasha tracks Kagome down and tries to take her back with him, but she school stuff to do, so they get into a fight on a sidewalk, inside a photo booth, while a crowd gathers to hear them. Sota puts in money to take pictures, so they can see how they are making a scene. Inuyasha even tried " Iron Reaper, soul stealer" on the booth, as it is taking pictures, and Kagome "SIT's him. It's very funny.
I believe you saw episode 38 and 39 where shippo drew pictures of Kagome in a Cat suit while he explained to Kaede what happend between Inuyasha and Kagome that caused them to fight and she ended up going home.
In episode 20, Kagome is wearing a yellow dress with a short sleeved jacket or something like that. She hugs Inuyasha because she noticed that he didn't come to see her in her world while he was wounded so when she finally returned, she was very worried about him.
Well my guess is that when Inuyasha saw her, he first saw Kikyo and then saw the real her later on. He basically had to met a whole new person that looked exactly like the girl that he once loved. As they went on with their journey he more and more got to know her and started liking her more to the point where he was in love with her.