Typos, not slow fingers, are what cost typing speed. Stop looking at your hands first, then how to practise, how speed is measured, goals and posture.
The usual reason typing speed plateaus is not slow hands but stopping to fix errors. One wrong character costs at least two or three extra actions to delete and retype. That is why moving accuracy from 95% to 99% changes perceived speed noticeably. Typing without mistakes ends up faster than trying to type fast. Setting an accuracy target and slowing down a notch whenever you drop below it works well.
Watching the keyboard sends your eyes back and forth between screen and keys, and that travel time caps your speed. Even if it feels slower at first, building the habit of not looking removes the cap. Resting fingers on the home position and assigning each finger its columns is the starting point. Speed dropping for the first few days is normal; getting through that period is the key.
What you type and how matters more than sheer volume. Repeating words you actually use often turns them into a single motion.
Korean typing is usually measured in keystrokes per minute and English in words per minute, where a word is conventionally counted as five characters. Because the bases differ, Korean keystroke counts cannot be compared directly with English word counts. Watching your own record change is more useful than comparing with someone else's number. Even for one person, results vary with the day's condition and the kind of text, so a weekly average is more accurate than any single score.
Forcing speed by striking hard loads the wrists and fingers. Keys do not need to be pressed hard, and keeping the wrist unbent matters more. Pain is a signal to check posture and equipment, not to add practice. A keyboard set too high, or a habit of resting your weight on a wrist rest, also adds strain, so check those too.
Typing practice works best when each stage has a different goal. At first ignore speed entirely and aim only to press each key with the correct finger from the home position. Once you can type accurately without looking, raise speed a little at a time. The point where accuracy starts to slip is your current ceiling, and practising just below it is the fastest way to improve.
Self-taught typists easily fall into piling work onto certain fingers. It feels comfortable at first, but the hand has to move further, which lowers the speed ceiling. Deleting every typo the instant it happens also breaks rhythm; during practice, finishing the word before correcting it protects the flow. If you keep missing the same combination, typing just that combination slowly ten times at a stretch works well.
If typing for long periods matters more than speed, sort out posture and setup first. Adjust chair and desk so your elbows sit at roughly a right angle, and set the keyboard height so your wrists do not bend up or down. During long sessions, shake out your hands and gently roll your wrists every thirty minutes to an hour. If numbness or pain lasts more than a few days, stop practising and see a medical professional.