The swords are indeed, longswords, and they can't be broken.
How long are they?
Her second weapon is secretly stashed under her sleeves. It is a blade that is around 3 feet long and it is locked onto her arm, and by just the right movement, the blade will shoot out of its titanium holder, cutting anyone near enough. When the blade is still inside its arm deployer, it can be used as a powerful armguard.
Okay the problem with this is that most longswords are about this size. That's really long, how would she be able to bend her arm? You might want to rethink the length.
Depends, how long is her arm? I'm guessing it would be on her forearm, right?
And now about the swords, three feet, that's big, she's kinda small. How light are they? Won't that be awkward for her to use? She doesn't use them at the same time does she? Does three feet include the hilt? How long is the hilt? How long is the blade?
You might want to consider making the handles a little longer, especially for such long swords. Do you have ruler handy? I find that helps me figure the lengths of my characters' weapons. No, I don't mind the affect you put on the swords. That's just fine.
You don't really describe what these numbers mean and on a scale of what. Plus, what kind of spells and abilities all this would entail. Explain it to me, and give me some soild descriptions on what she can do with this elemental magic.