Pushing for ‘skinship’ or something more intimate too soon will cause her to doubt your intentions.
If you are a white, young, and somewhat handsome, male then a lot of Korean girls will quickly and automatically judge you as some sort of playboy or womanizer.
They know as a foreigner in Korea you attract a lot of attention and they may assume that you must have many girls chasing you.
They will certainly start any relationship with suspicion. Early on, you may find that your new girlfriend will want to check your phone for evidence of you seeing another woman.
The best thing to overcome loneliness and improve your adjustment to the country would be to start dating a Korean woman.