Law schools care mostly about grades and LSAT scores, so moving to a different university isn’t likely to be a problem.
Since you are miserable socially, a semester off to re-group and consider options could be in order. Think about that too. You could get a job and/or do some volunteer work while you think things through.
There also could be the option to do a domestic exchange semester or year. Have you investigated that?
Could there be good academic reasons for you to transfer? For example, does the “inferior” local U offer courses that you can’t get where you are now?