A 15 handicapper like me will spray their drive more than occasionally probably miss the green in regulation, chip up and hope to one putt for par. So short game is important to me - I need to get the ball on the green (with practice get it somewhat close to pin). I say short game is most important to me. A single digit player makes more 3 and 4 footers, hits more greens in regulation because of longer drives that land in fairway.
??????? Short game is more important ????
I suggest finding a Par 3 course and play it until you can shoot below you handicap.
This will sharpen your short iron / wedge play and putting skills.
Once you have confidence in this aspect of your game, you should then see if you can maintain a lower handicap?
You will still have difficulties due to lack of improvements in your long game !!!!!!!!!
The game requires a player to preform every single aspect, tee shot, approach, play around the green and putting skills.
And, it don't come easy...........