If the squeaking is coming only from that floppy, I'd back it up and toss it. If it's the drive (it squeaks on other floppies including new ones), you might need it replaced as a last resort.
Most likely there's 2 pieces of cloth inside to keep it from making noises and sticking. From the excessive wear & tear it can break apart and begin to cause problems.
If you know how to clean the heads of the floppy drive, go for it. Probably that may help as well to reduce dirt from them.
Hope this helps!
