I'm sorry this happened, Abby & Kiki, but am so glad you were there to catch it. I am very cautious about any type of toy, perch, or hut with cotton. I check for loose strands daily. For birds that are shredders of cotton, I don't even use cotton perches, but the sisal ones instead.
I think you should take your girl to your avian vet if she behaving differently, and possibly the emergency avian vet tonight. Better safe than sorry.
Donna, that's a horrible thing that happened to your bird. I'm so sorry.
I've never heard of that happening before, so I have learned something new.
As a general rule, I find fleece to be much safer than cotton, whether it be in toys or huts. I don't use huts for my birds at all because I don't want to promote egg laying in my girls...did that recently, and took away all huts. Most of my birds really love to sleep on their fleece swings.
As long as we're talking safety, I thought it was worth mentioning that you also have to be careful with chains with some birds, especially the big birds. Some birds are prone to getting toenails caught in the chains. Then there are quick links...these should be checked daily to be sure that they are always closed. Lots of birdies like to open them, but they can quickly become a safety hazard for a foot or two to get caught. Some people like to take leather strips and weave them in and out of the chains as a safety, preventative measure.
Basically, any and all toys can be a potential hazard to our birds, so it's best to do a check of all toys to check for loose strands, etc. daily.
Abby, I sure hope Kiki feels better soon. Hugs!