It depends on what kind of game developer career you are seeking. Most titles created in the modern game industry are made by huge teams where a programmer doesn't ever have to draw a single pixel.
Though if you're more into developing your own indie game, you could assume the "one man army" role, in which you'll have to deal with graphics and sound creation. Take a look at my own title, for instance: https://chromewebstore.google.com/detail/empty-title/ggglioliiaplkedaddaanpenblibggnp
Programming was the easy part, while generating synthezisedsynthesized sound effects and drawing pixel art consumed most of my time. Thanks God for public domain music which in this case perfectly suited the whole groove of the thing.
If you grew up in the 80's when you could actually see pixels on the screen (and then never being able to ever ignore them later) it could just grow naturally on you, but if that's not the case, I'd recommend reading a bit on pixel art creation. Of course you can always digitalize some paper drawing and just do the finishing later.
Anyway, creating games has always been a multidisciplinary craft. You'll need a good depth of programming skills (but not 'too much', or you'll end being unable to create the simplest game, because you'll be over-worried about abstractions, just like a good grammatician can't write a single book), good understanding of math, geometry, physics and also a good deal of artistic skills, like drawing, sound creation, level design, story telling, etc.
Ultimately, you must fall in love with your creation. You need a good deal of motivation and a genuine desire to make your game see the light. You must become the #1 fan of your own game, because if you don't like playing it at all, who else will?
With all that in mind, I really hope you overcome your obstacles and have a great time creating your own game. It's an incredibly fun and rewarding experience once it's up and running. :)