l enjoyed your video.
I play concert size, and though I don't have your pain issue, I did injure all my fingers. so have some permanent damage from that. Lower tension strings help, and being very particular about the ukulele neck helps, (width, thickness, set-up, and so on.)
Favorite strings for comfort AND sound: Living Water and Uke Logic. But it sounds like you might not like that type of string?
You might need to take a break from playing for a bit, but if it's just your fretting hand that is a problem, you could still work on right hand technique while letting your left hand heal, (reverse that if you're playing left handed.
)
The site you linked to was a good reminder that warm up exercises are important. And that we should pay attention to how much pressure we're using. I need those reminders.
You can try tuning down a little bit. If you're not playing with others, it doesn't matter if you tune down 1/2 step, 1/4 step, or whatever works for you. That will give you less string tension.
It may take some experimenting to find what helps you, but hopefully, you'll be back to playing without pain soon.