High School Frenemy is the actual Thai version of School 2013 Korean version. I'm a bit surprised it's not part of the recommendations.

One of the two leads, after being warned of something dangerous in the future, he & his lover are chased by criminals into an alley that sends them into the past during the 1890s or 2433 Buddhist era. This is where they must adapt to their time there and find their way back to the present day.