That bridge will probably NOT work, as it is meant to be screwed onto a frame with the same bridge-type. The 2 little holes are there for the screws to go through, and the right frame will have 2 little “female” ports for the screws.
Going forward, NEVER modify a broken frame or attempt repair yourself. Doing so voids any manufacturers warranty that may have been in effect. Too late for that now, and you had no way of knowing. For the most part, a LOT of frame manufacturers offer a “defect warranty”, and to be honest, a broken nose-pad arm can often be “passed off” as a defect, especially if it’s very close to the solder point. If the frame is less than a year old, I’d take it back to the point of purchase and see if they can pass it off as a defect and replace it under warranty. Be sure to say, if questioned, that the break happened over the weekend, and you couldn’t get the glasses to the optician, and it hurt the child’s nose to wear them with the sharp metal. Otherwise, call around to local opticians and find out if anyone solders frames (a rare thing, these days). Anyone who solders will probably have some “parts” lying around that can be used to Frankenstein the glasses to hold your boy over until his next new pair. “Ols school” opticians would be your best bet for this, or, oddly enough, a jeweler. You will not get someone to solder them in any type of mall store.
Also, under NO circumstances should you attempt a repair with super-glue. More often than not, it will do more harm than good, especially when it gets on the lenses and can’t be removed. I’ve seen $600 eyeglasses destroyed by one drop of glue.
If all else fails, you can either just buy a new frame, or just remove the other nosepad arm. Removing the arm will result in the metal resting on his nose, which can cause problems (corrosion from salt in the skin will create pits in the metal and scratch his nose). If you have to resort to removing the arm, I strongly recommend a very careful application of clear nail polish on the frame wherever it will touch his nose, to prevent the possibility of corrosion. Reapply nail polish occasionally as it wears off.
Will check in on thread again, in case I can be of help.
22 years in the optical business