do i get ban if i open my mylot account in a public computer?

No, there's no reason why you should be banned if you open your account on a public computer. Make sure, however, that you close it properly when you leave and delete cookies and other things that may mean that anyone else would be able to log on as you. 'Tools/Delete Browsing History' is the way to do it in Explorer 7. Otherwise you should find the facility in 'Tools/Internet Options'.