So I've had a leak somewhere in my coolant system for a while, just been filling it up when the buzzer goes off, but a few days ago it all of a sudden got really bad, and I finally found out where it was leaking from:

http://youtu.be/sO8S0j4WH-I

It's not obvious in the video, but the spot on that tube where the water was spitting out from was kind of hanging over on the metal piece that's on the side closer to the engine, so I used a screwdriver to snap it back into the groove where it's supposed to be. This didn't stop the leak but it seemed to slow it down.

Is this something I can fix myself with some JB weld or something?

 

Yes, fixing it yourself is easy.
1. Buy a new radiator
2. Remove and replace old radiator.

Although your explanation of ...tube..hanging...metal piece indicates you might want to pay for the service. Even a piston mechanic can replace the radiator.

You should be happy your radiator lasted 20+ years.

Replace the hoses and belts while you're at it.

 

like cone crusher said, the seam of your radiator cracked and broke. replace and you'll be good.