It would be helpful to know a bit more about each school.
Is your current school a small LAC or a large university ?
If a small LAC dominated by Greek life, then a transfer might be a wise move.
If you currently attend a large university, then there should be many options to meet others who are not into the Greek party scene.
Although lonliness is not uncommon when moving away from home & adjusting to a new life at a college or university, some people just function better in different environments.
Just by applying to transfer you should experience some relief because you are taking a step to help yourself. Nevertheless, it is important to make the most of your current opportunities. Joining a club and a religious group are great efforts to assimilate on your part.