Caitlin, I experienced the same issue as you describe, on me and it was random. When I detected it, I took everything off and there was no issue with any attachment in my case. I logged off and also I deleted some of the files that SL maintains between sessions in the PC (maybe this list is not comprehensive, but these are the files that I delete from the Temp directory I defined in SL:
del *.dsf
del avatar_*.*
del *.inv.gz
del data.db2.x*
del index.db2.x*
del name.cache
del *.cached_mute
del experience_cache.*
del texture_list*.*
rmdir texturecache /S /Q
rmdir objectcache /S /Q
rmdir cef_cache /S /Q
Then I logged back to SL and the movement of my hand was gone.
Maybe you can expand and fit this workaround for your specific case.