I think there is some kind of periodicity in people asking this kind of questions :)
Nevertheless, I don't get the point of your questions, especially in
I don't really know what studying category theory at a higher level involves.
I mean, if you really studied some CT, you've already seen that its language subsumes practically every kind of Mathematics (or even some parts of Physics) you can study or imagine to study; you can turn general theorems into Differential-(Algebraic-) Geometric results, you can give the most general setting in which develop homological algebra, you can do Homotopy Theory at your favourite level of abstraction, you can use (Mac Lane & Moerdijk do so) sheaves in Logic, you can see abstract and universal Algebra from a wonderful perspective... So there's no way (for me, other people surely have a better intuition of what Category Theory "is") to give you a unique answer to this question. The good side is, you see that you can do fairly everything if you study "CT at higher level", just as you can potentially speak every known language if you "learn" basics of moving your tongue.
I see from your profile that you're an italian student from Milan; I'm not very far from there, living in Padua. It seems to me that Category Theory (as a branch of Mathematics per se), in Italy, is not really developed (to tell the truth, I seriously hope somebody will contradict me!). It is deeply intertwined with two of the topics I mentioned before, namely Logic and Algebraic Geometry; analysts don't get the point in "categorifying" their thoughts, physicists hardly know the definition of a sheaf (in my experience, even of a smooth manifold). In my opinion this is due to the fact that CT "can hardly walk alone" its path, it needs to give insights to other branches of Mathematics, as it needs to pick up examples in Mathematics seen as a whole subject.
As a (highly non-genius) student labouring from some years on the topic, the most useful advice I can give you is: He who loves Category Theory thinks Mathematics as a single, huge subject: so, if you want/can do it, learn the more Mathematics you can see, in the more wide range of topics you can reach: then Category theory will give you lots of insights. If you jump over this step, I think you'll feel like a blind man seeking the colour of the grass.
Sorry for this long stream of consciousness: in fact any answer I can give you highly depends on your answer to the following question:
Why do you like CT? Do you want to use it to answer other mathematical questions (e.g. in Geometry, Topology, ...)? Do you want to reach via its language a more precise idea of "what Mathematics is" (for example enlightening your view of Logic or foundations of Maths)?