When I was young I read a book about a teenage boy whose life was very miserable because his mother had died. He then finds a girl in his house and she thinks she is in her house. They share about their life and find out that they are the same person but in different dimensions.
They realized that every decision and choice had 50/50% chance of happening. He was envious that her mother was still alive and his mother was dead.
A Crack in the Line by Michael Lawrence, 2003, first book of the Aldous Lexicon?
Alaric
It's been two years since his mother died in a terrible train crash, and Alaric's life continues to unravel. He and his father are barely on speaking terms, and Withern Rise, their Victorian mansion, is in shambles. Trapped at home during a blizzard, Alaric stumbles into a parallel world; a reality in which his mother is still alive. There's only one problem ... someone else is living his life.
Naia
Naia tries not to dwell on the horrible accident two years ago that nearly took her mother away. Now that life with her parents in Withern Rise has returned to normal, Naia thinks the worst is behind her. But during a freak snowstorm she's confronted by a stranger. Why does this boy look like her? Why does he have the same thoughts? The same memories? Who is he?
Don't know when you were a teenager, but vaguely seems like maybe a scene that I believe I recall from Interworld (2007). But I don't have a copy handy to double check that the particular details of the alternate dimension you are describing match up.
I am certain the protagonist meets a female version of himself in his early dimension hopping. I recall his mother was not healthy. I recall him being envious of some of the good aspects of the alternate dimensions he visited.
The Many Worlds of Albie Bright by Christopher Edge
When Albie's mum dies, it's natural he should wonder where she's gone. His parents are both scientists and they usually have all the answers. Dad mutters something about Albie's mum being alive and with them in a parallel universe. So Albie finds a box, his mum's computer and a rotting banana, and sends himself through time and space to find her...
Around page 120:
This other Albie turns round and my jaw drops to the floor as I see a girl staring back at me. It’s like looking into a funfair mirror. Her face looks the same as mine - eyes, nose and mouth all the same shape and in the same place - but she’s definitely a girl.
