I think there is something wrong with my floppy drive. I can't read the disks it writes in other drives!

If you are having problems reading a disk on one drive that was written with another, it may not be damage as such.

Firstly, is it a "Magic Pack" Amiga?

If it is not, it could be that the drive is not spinning at (even near) the 300 RPM that it should be, or it is out of alignment. There is a simple test for this; Format a disk with your problem drive, copy a file onto it, then see if you can access the file using another drive, and try doing the same thing the other way round. If each drive cannot read the disks of the other, you have a drive speed/alignment problem.

You may be able to fix these problems yourself, but it is probably still easier to source another drive.