When my fingers hurt after too much time on the keyboard, I just take a break and come back again after 15-30 minutes.

My tip to improve your typing speed is to keep on practicing . and as cliche as it may sound. you gotta focus on your accuracy rather than focusing on speed and messing up your accuracy.
You keep typing accurately. and you'll notice how your speed will get better.
One more thing is that you gotta understand that the progress is not linear in typing. some days you'll be slow. some days you'll type faster than your normal. then again you'll become slow.
So, don't worry if you see such highs and lows in your progress. eventually your speed is going to improve if you just do the 2 things i mentioned above.
1. Keep practicing
2. Focus on accuracy