How do I get my hair to grow strong?

My hair used to be quite long. It used to go well past my boobs and it was pretty healthy... It's always grown reaaaally fast!

This March I bleached my hair blond.. luckily it didn't fall out or anything but it went really dead.

I didn't want to bleach it again when the roots came through cause I didnt want to damage it more, so I dyed it back brown and had it cut to just past my shoulders. (This was in July)

Now its almost 4 months later and I know that my hair has grown because my roots are coming through (and it's not just a little bit, its like 3/4 inches) but my hair is still the same length as it was when it was cut...

My mum says that the ends might be snapping off because of the bleach before, but I never notice it.

So can anyone tell me why it's growing but not actually growing?

And is there anyway that I can make the ends of my hair strong again so that they dont snap?