Practice makes perfect, 3-4 months is no time at all.
In 3-4 months and good determination a person can learn shitload of stuff.
I learned most of advanced c++, basic java, SDL API, sfml API in time of 6 months.
To top that all i started about 100 projects finished about 30.
And cream on top, I work 10 hours a day 20 days in month...
The reason of my success is " I just love writing/reading code! ",That is what you really need, programing to not be dull process.
I am not finding myself having a hard time learning this.
Art is out of the question my art skills suck
Art... Well as you stated you want to be a programmer not a artist. Download free art, give credit to artist and use it in your game... simple!
EDIT: If your don't feel confident enough to jump to a API and use it.
Try making you self a goal to make something somebody could actually use or,
A calculator that handles "Adding" in console.
then add "Subtracting"...
The point is to train how to make stuff. You will stumble on "difficulties/how to make that" and solving problems is important in programing.
After you done that, try thinking of a way to improve the code you made to make it more efficient.
Hope it helps.
I've been programming for 18 years, i'd say 3-4 months is pretty much nothing(at uni i had people who couldn't grasp things properly after 4 years), people learn at different paces and spend different amount of time learning (Lots of people have more than one thing that occupies their time when they're not working / going to school)