Pursuing the field of computational physics professionally with a physics PhD
So for starters, I want to comment on your interest in writing everything from scratch. I feel for you with that, I felt similarly when I was starting out. While writing codes for some things that exist in great software packages already can definitely make sense, I will specifically say that writing code to do numerical linear algebra work is a terrible use of time. These numerical linear algebra packages are optimized to the extreme both with respect to algorithm approaches and with their software implementations. 

Now implementing some of these things yourself is a great learning experience but don’t expect your code will perform nearly as well as the popular and proven packages. Also note that when it comes to being a productive researcher, you will have to be smart about optimizing your use of time. Building up your own numerical linear algebra package is likely not going to be a very productive use of your time. Feel free to comment.

As for how to learn, you should see if you can find more specific courses in other departments in things like computational mechanics so you can develop some general computational science skills, if you cannot find computational courses with your desired niche. From there, you’ll want to find some good textbooks to supplement your learning, depending on what things you need to learn more deeply or that fit your domain of interest better. You’ll obviously want to also develop some of your own solvers after you’ve covered the theoretical side of things to validate your understanding. 

Outside of the straight up computational physics learning, you should try learning about some topics that could be useful, such as High Performance Computing, numerical optimization, and perhaps some minimal computational geometry.