I believe the anime you may be describing is Shakugan no Shana. I am pretty sure this is the anime your describing as this takes place in Episode 1 if I am not correct.
The two creatures discover that Yuji can move about in the Fuzetsu, and deducts that he might be a Mystes. Curious about his identity, one of the creatures grabbed Yuji and attempted to devour him... until a blade slices its arms cleanly off. As the gigantic baby doll cries in pain, Yuji finds a girl with blazing-red eyes and hair standing in front of him. Soon, she confronts the creatures in front of her and mercilessly defeats the two. The girl with blazing-red eyes soon ask about Yuji's existence, and like the creatures she defeated, a voice she refers to as "Alastor" assumes that he is a Mystes. Then, she attacks another creature; this time, it is in the form of a woman, and that creature mockingly identifies the girl with blazing-red hair and eyes as the "Flame-haired Burning-eyed Flame Haze of Alastor, 'Flame of Heavens'". As the Flame Haze is about to deliver the final blow, a confused Yuji goes in the way, and is instead attacked by the enemy. Leaving with no choice, the Flame Haze strikes her sword and tears a large gash off Yuji's shoulder, slicing off the enemy's arm in the process. Shocked by the attack he receives, Yuji falls to the ground as a small doll-like figure escapes from the scene.
(Summary of Episode 1 per the wikia since I couldn't remember entirely what happened in episode 1)
Also Yuji Sakai says this quote "That was the day my world ended" which was actually "That was the day my world...changed forever." which happened at the end of the episode. (src)
Also known as Shana of the Burning Eyes
He had thought his normal days would last forever, until they were ended abruptly by an encounter with a girl with red hair and eyes. He named her Shana.
Not long after he enters high school, Sakai Yuji’s normal days come to an end. He sees something bizarre on his way home: people are frozen in a strange fire, and a monster that looks like a large doll is attacking them. Just when he's about to be killed, a girl in a dark cloak wielding a large sword appears, and slices the monster in half. Although Yuji survives the strange encounter, the girl informs him of a desolate truth: " 'You' don't exist anymore."
She calls herself a Flame Haze who hunts "Guze no Tomogara"; intruders from another world. She explains to him that he is a "Torch", a substitute of Yuji whose “existence” has already been devoured. She also told him that he is a special Torch, "Mystes", which contains a precious item in it. When he looks at his chest, he sees within himself a faint flame, just as she said.
It is in this way that his eternal struggle alongside the girl begins.