@mathandcs thanks a lot for the insight! That brings another question (about double-majoring) but I’ll post that as a different question (so nothing will be confusing).
I want to point something out. In this similar (but not same) thread: http://talk.collegeconfidential.com/graduate-school/1769348-undergraduate-master-and-phd-from-the-same-college.html#latest
@juillet wonderfully explains that it may be ok to study in the same university if that university is already one of the top schools in the area (as I explained, my case is similar). But my question was a specific “Can I get in / what are my chances?” type of question. So thanks for your answers!