Sean Caroll's book is one of the best books available for an introduction in GR. However, in order to trully understand what GR is about you will need to learn some essential things regarding differential geometry. As you may already know, S.Caroll's book "Spacetime and Geometry" covers these mathematical prerequisites in its first chapters, before introducing GR to the reader.
The first thing a physicist should do is try to find and learn only the trully essential elements of differential geometry needed to understand GR. In my opinion, it would be a waste of time to try and master differential geometry as a whole. For that purpose, I believe that the book you mention is very good as it has gathered these essential elements of diff. geometry and nothing additional (by additional I mean that nothing you learn from this book has no use in the study of GR).
Unfortunately, I do not have a better book in mind. The other books and material I know are all more advanced in the mathematics and, thus, harder for a high school pupil to cope with. I hope this helped a little.