You can definitely do this! I went to school for Computer Science, and I can recommend that in terms of a future career.
But also, it'd be immensely helpful to start experimenting on your own making small games either with Python, Godot, random javascript websites, "helper" apps like Game Maker, or even something like TI-BASIC programs if you have a TI-84 calculator. By the time I got to higher education, I already had a good amount of experience from playing around, and that really helped learn more complicated concepts later.
For Godot specifically, I can recommend looking at some of the starter templates, and challenging yourself to change some things like, the character jump height, or firing speed, etc.