How terrific that at least one course bowls you over.
The reason you keep discovering you need tools from one "branch" of mathematics to proceed in another "branch" is that there really are no branches. There is just mathematics and it is all thoroughly intertwined. We split things up so that we can teach them, or focus on them, but any split we make is at least partly artificial. So just about the time we think we've learned geometry, someone comes along and solves our hardest problem with algebra. Or we're working away at number theory, and someone brings our attention to elliptic functions.
The mathematicians who accomplish the most are the ones who know the most, and the amount, depth and breadth of what they know is amazing. So if you want to be really good, the answer is you just keep on learning, as much as you can in as many areas as you can.
However, you must also survive graduate school.
To deal with the courses you are less interested in I suggest (after years of experience doing things I don't like) that you attend to what needs to be done for those courses first. Do what you have to do, but not more.
Then plunge into what you like, and do more than you have to do. Discuss the interesting stuff with others who are also interested. That is a huge motivator.
Now -- do you want more of a life than mathematics, or not? The best mathematicians spend huge amounts of time on the subject. They work all day at it, then at night they go home and for recreation they -- do more mathematics. Is that the lifestyle you want? (I'm not knocking it, it's either for you or it isn't.)
If the answer is yes, you will have plenty of time do learn tons of math. If the answer is no, you have to budget your math time so it doesn't take over your life. And that definitely means concentrating on what fascinates you.
The good news is that what fascinates you is entrenched in mathematics, and as you concentrate on it a lot of peripheral knowledge will just naturally come to you.