You must have heard by now the phrase, you can do anything if you really want to, well, Programming is definitely one of those things, if you are an arty person, your programs will probably be very stylish and look the best, you'll no doubt have the best graphics, but maybe the content or the technical side of your program may not be so hot, if you are logical, this should come to you quite quickly. You may never be the best programmer in the world, but there is no reason as to why you cant make some programs which work.
Every program is made up of many parts, generally now no longer is a programmer just expected to hack away at the odd routine, most programmers now are expected to be involved in designing the program, producing documentation (if in a commercial environment), manuals, help files, maybe even the training courses! Being a programmer is no longer a form of technical typist, you need to be a lot more versatile.