Becoming a better putter takes a shift in “focus”. Better equipment and practice plan over a couple of months will help.
First is your equipment. So make sure the putter is fit. Putters that are too long cause big angles in the elbows and putters that are too short make the arms to straight and stiff. Find a putter that lets your elbows be soft and have a slight bend.
Second, you will need to choose between a classic blade head or mallet. Over the years I have putted with both. What I have found is mallet heads tend to help players who have stroke deficiencies, and blade putters help with feel and touch inside 10 feet, especially on fast greens.
Last, is the grip. More players seem to opt for the bigger grips like the superstrokes which help eliminate wrist action. This can be good, but at the same time detrimental if you struggle with feel and speed control.
Whichever you choose, make sure it is based on your performance inside 9 foot, not 30 foot.
Putting is more art than science. Player whose putts finish near the hole from all distances will tend to out perform those who spend the majority of their time worrying about stroke shape, alignment and green reading.