Otome game

After finishing your classes at the institute and a grueling day at your part-time job, you finally arrived home. Exhausted and sleepy, you collapsed onto the bed, having only taken off your outerwear. But there was a problem: sleep wouldn't come, and you had no sleeping pills.
After a few minutes of thinking, you picked up your phone and, after browsing through many games, downloaded an otome game. Once it was installed, you immersed yourself in it, forgetting about the time and the coming day.
An unknown number of hours passed; you completed the main story and the routes of the supporting characters. Now, you are trying to complete the story of a side character who dies on the way home.
Ugh!
You exhaled in frustration and tossed your phone to the other side of the bed, as for the fiftieth time, you couldn't save the character from death and progress in the story.
Closing your eyes, you seemed to fall asleep, but the feeling of someone's presence forced you to open them—only you were no longer in your dorm room, nor even in your own body. You were inside a carriage that was moving slowly under heavy rain and large hailstones.