The main character is female, and she has to take part in a race to get some cure for her mom (I think). At the beginning, she gets some kind of message, letters I think, and leaves her house without her parents permission. All the participants get an egg, I think, that hatches a creature. The male love interest is named 'Guy'. I'm pretty sure she doesn't win the race and her creature that hatched died. It was a series of books, I think its probably a trilogy, with the titles being 2 of the locations of the part of the race that occurs in the book.
Fire & Flood by Victoria Scott
Tella Holloway is losing it. Her brother is sick, and when a dozen doctors can't determine what's wrong, her parents decide to move to the middle of nowhere for the fresh air. She's lost her friends, her parents are driving her crazy, her brother is dying--and she's helpless to change anything.
Until she receives mysterious instructions on how to become a Contender in the Brimstone Bleed. It's an epic race across jungle, desert, ocean, and mountain that could win her the prize she desperately desires: the Cure for her brother's illness. But all the Contenders are after the Cure for people they love, and there's no guarantee that Tella (or any of them) will survive the race.
The jungle is terrifying, the clock is ticking, and Tella knows she can't trust the allies she makes. And one big question emerges: Why have so many fallen sick in the first place?
Victoria Scott's breathtaking novel grabs readers by the throat and doesn't let go.
A reviewer mentions an egg and Guy:
I loved when Tella got there, got her egg and got on with where they had to start the game. And I fell in love with her Pandora, which comes from the egg they get in the beginning, he was a little fox, but he has some things he can do :)
I loved Guy, he ended up being Tella's love interest and his pandora was a lion.
Found by googling: young adult fantasy novel guy "race" egg