The Importance of Putting
Consider par: the evaluation of how many strokes a highly-skilled player would take to get the ball in the hole to have an excellent score. It's based on the length of the hole plus two putts -- always two putts. If there are 18 holes on a golf course and each green is worth two putts that means that par for putting is 36. The majority of 18-hole golf courses are par 72. That means that half of par is putting. That's an interesting way to look at it.
Here's another interesting way to look at it. Consider the best golfers in the world: touring professionals. If the average number of greens in regulation for touring professionals as a group is approximately 12, that means that they are missing approximately one-third of the greens. But the average score for touring professionals as a group is very near par (perhaps even slightly under par, depending on which particular group you look at). The most blatantly telling statistic is putts per round, and the average number for touring professionals as a group is less than 30. That's how the average score gets back in the vicinity of par even with all those missed greens.
So the importance of putting cannot be overemphasized. Acknowledging that touring professionals play, practice and work on their games pretty much day in and day out, and realizing the complexity of the full swing and the general lack of control over the outcome of longer shots, do you think that your best chance of lowering your score, given the amount of time you have to practice, is with the long game or with the short game? Since the best players in the world can only manage a two-thirds success rate at hitting the greens the answer is fairly clear. Your best chance of lowering your score lies with the short game, beginning with putting in particular.
There is good news about focusing on your putting and short game: skill development and the reward of lower scores can happen much more quickly than with the full swing and the long game. And once you combine putting with chipping, and then pitching, and then greenside bunker play and the rest of the short game, the effect on your score should be substantial.
Start keeping track of how many putts you have on every hole and total them at the end of the round. Keep a running history of your putts per round. Also start doing everything you can do to improve your putting and your short game.