I heard my Sun Conure chewing something and realized it was one of the little metal things that go along edges of zip up jackets. I tried to get it out of her mouth but she swallowed! Should I be worried?

Yes!

Take a good look around and make sure she didn't drop it. If she did drop it
thank your lucky stars.

The problem is what kind of metal it is and if it is sharp and whether it is large enough to cause a blockage . You really need to talk to an avian vet. Lets hope you find the piece of zipper.

keep looking for vets it worth ur featherd freind

I'm sorry. Thats awful. It happened to me once. My bird bit through a gold link chain at midnight and I thought she swallowed it. I couldn't get to the vet. I was certain she ate it but she didn't die. I think it must have fallen on the ground and in my panic I couldn't find it. Keep looking for vets, but there is some hope for her if you absolutely can't find one.

I hope everything turns out ok.