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All I remember is that a few kids, I think there were two boys who were best friends and maybe their female friend, would somehow transport to a place where they would compete against other kids in virtual reality by fighting as monsters/creatures with special powers. I believe each character could only fight as one creature that was their own, and they could upgrade their creature. This aired in the late 2000s or early 2010s.

Ohhhhh... it's called Chaotic!

The Wikipedia description says:

Chaotic is an American-Canadian animated science fantasy television series.... It is based on the Danish trading card game of the same name. Much of the plot is based on the original storyline of the Danish trading card game

...

Chaotic tells the tale of a teenage boy named Tom and his friend Kaz. They both play the Chaotic Trading Card/Online Game. Kaz always tries to tell Tom about a secret code to play for real which Tom refuses to believe. While playing online Tom receives the special password. When he enters the password into his game scanner he is transported to a place called Chaotic that is able to take him to another world where the characters, locations and items in the card game came to life.

There are two parts to the Chaotic world, Chaotic itself and Perim. Chaotic is where the people play an advanced version of the card/online game where they transform into the creatures. The games can be watched via monitor by other players.

The second part is Perim. In Perim the creatures, locations and items from the game are real. Players from the Chaotic game can teleport into Perim and scan the locations, creatures and items with their scanners, gaining the ability to use them in their game. There are four tribes in Perim. Two tribes, the Overworld and the Underworld, have been at war over a great power called the Cothica.

This sounds vaguely like Legendz, a Pokémon-like anime from 2005. In it, three main kids, two boys and a girl, fight through monsters with others. The “Legendz” monsters seem to grow, too, based on this Amazon listing:

...any kid could raise them and train them to play the ultimate role-playing game?

Found based on my limited knowledge of Legendz and info from Wikipedia (all I really knew was it seemed like a 2000s Pokémon ripoff.)