Pokémon Ultra Moon was my personal favorite Pokémon game since it really introduced me to the world of Pokémon. After seeing a one shot use a Pokémon AU idea, I decided to make my own personal head canon for an Ereri Pokemon Sun and Moon alternate universe. Just to make it clear, I will add backstory to this since I don't want it to just be Eren and Levi, but I wanted to also add some of Eren's friends.
Eren's Team
Poppolio➡️Brionne➡️Primarina
Pikipeck➡️Trumbeak➡️Toucannon
Eevee
Pichu➡️Pikachu➡️Raichu
Levi's Team
Mankey➡️Primeape
Zubat➡️Golbat➡️Crobat
Salandit➡️Salazzle
Type: Null
How they both met: After Professor Kukui gave Eren his starters, he decided to head over to the trainer school since it was an absolute need if he wanted to participate in the island trials. One day, he was outside playing catch with Poppolio until it knocked the ball a bit too far and landed in the tall grass, over the fence. However, when he went to get it back, he accidentally landed on another student who was training in there. Eren got up and apologized and retrieved his ball, but before he left, the student (who introduced himself as Levi) insisted he and Eren walk back together. After they walked back, they both noticed that Poppolio and Levi's Mankey had shown interest in each other as buds. So, they decided to become friends and from that day on they were insuperable.
How they helped the other when they felt dejected/unmotivated: It was no surprise that Eren would not pass first totem Pokémon on his first try. Mikasa, Armin, Jean, Connie, Sasha, Ymir, Krista and basically all of his friends had passed on their first try. When Eren failed to pass the first time, he ran away to the Tapu Koko Ruins and sobbed. He stayed there for a couple of days, refusing to leave. Heck, even good ol' Hala couldn't convince Eren to go back home. Back with the group however, Levi was acting different. He snapped at people more often and was even caught laying curled up in the tall grass, wallowing in despair. He also trained more often, which triggered his Mankey to evolve into a Primeape. The group had to convince Levi to go see Eren, telling him it would make him feel better. So, that's what he did. However, he went to the Tapu Koko ruins when it was storming out. When he saw Eren, he immediately pulled him into a hug. A strong gust of wind knocked them both over the edge of the canyon and they both got sent tumbling down. Fortunately, they both were rescued by Tapu Koko who rewarded them both with Z-Stone Rings because it felt that they deserved it. Eren decided to re-do the first trial and passed.
Having the effects of a Pokémon and how Levi reacts to this: During their time on Akala Island, Eren had fished up a Pokémon. This Pokémon was a Luvdisc, a Pokémon notoriously known for blessing a couple with love. While Eren and Levi were not dating, Eren's desire for Levi had triggered the Luvdisc to release a hormone that made Eren want Levi more than ever. When Eren came back to their hotel room later, he noticed that Levi was taking a shower and had left his shirt on his bed. Eren, being under the hormone's effect, snatched Levi's shirt and gave it a deep inhale. He continued to nuzzle and smell the shirt until he saw Levi looking at him, still shirtless. Eren couldn't control himself or his actions in that moment, so he roughly kissed Levi and pushed him on the bed. Levi somehow got on top of Eren and let's just say that after that night, they were dating.