If I transfer to a public school in second semester, will universities not like it?

Universities will be very curious as to how you will do when you switch schools. If you are doing well at the school you are in and transfer to another, seemingly more challenging school, and do just as well or better, this would certainly point out to them that you do well in changing and transitioning and would likely do will in the transition to college. Colleges look for improvement and aptitude, not absolute perfection. They would rather take someone who shows great potential than the one whose spark may have hit its apex already!