Firstly like with engineers there is a spectrum of "professional graphic designers" out there from the bad where the most they can do is merge various images in photoshop to the amazing who produce award winning add campaigns. However as I said to a friend once, everyone can draw, to be able to draw well enough to get compliments is a skill and to do it well enough to get paid to do it is a talent.
Also similar to engineering the basis of the craft is a combination of understanding of a toolset and a knowledge of accepted theory. So as a graphic designer this would be a working knowledge of the tools of your chosen media, in your case digital imagery using photoshop, gimp etc. The theory would be proportions, perspective, colour theory, typography etc. This can all be learnt, though it may take some time. Mastery of these will leave you as a competent graphic designer.
However good graphic design can be said to follow the Pareto Principle 80% is theory and tools the remaining 20% is artistic vision, and its the artistic vision where the money is. "The vision thing" isn't as mysterious as it sounds. Partly this is just experience with the designer producuing a synthesis from their experience of other work and partly it's an application of human psychology; and off course there is that special X factor that makes the truly great truly great.
I would suggest to start with ditch photoshop, gimp etc. and concentrate on the theory and experience parts. You'll gain more sitting with a pencil and a stack of blank paper and sketching than you will learning how to crop and interpolate an image in photoshop. Read up on the theory and try and apply it:
-The classic example of perspective is the view down a straight road, read the basics and pop outside and try and sketch one.
-Get out those paints and start mixing them and contrasting them to explore colour theory.
As in programming the more tools/languages you have the better, so explore other media such as sculpture and collage. As you can see a lot of this is experience and practice; practice with constructive feedback, so if you can find a local evening class or group to provide it externally even better.
While your doing all this you should look at what others have done around you. If you see something interesting on the street take a photograph, if there's an interesting bit in a magazine tear the page out and keep it, visit a design museam, look over the design books, all of these are building your "ideas bank". Later you can use these, partly for inspiration, but you can also try copying and then altering and extending them. The art world has a fine history of this kind of plagarism.
To sum up, to be good you need to master the theory and develope a knowledge of the environment. The tools used to achieve this aren't important and you should use the one you are most happy with, learn other tools later when they become useful to achieve what you want to achieve.