I think both are great! Design schools have a lot to offer because you will be exposed to many different ideas in a short amount of time. However they can also be very expensive and depending on your skill level and you can’t make a living being an graphic artist right out of the gate, at least not in my experience.
I suggest start small. Build your own website, learn everything thing you can for free and see what interest you. I began with CAD drafting and design. Autocad and technical drawings paid well and and that moved over into graphic design over time, many many years later.
I still love doing it and it has been very satisfying. I wouldn’t change a thing. It allows me to be creative and it paid the bills. It doesn’t seem like work and it is something I truly enjoy.
After CAD and graphics, I expanded into laser engraving which also proved to be very rewarding. The funny thing about graphics and design you can change into different markets without losing experience. Flexible enough to change from oil and gas to automotive to web design and never miss a beat.