I have a loud squeaking noise from a GE electric dryer drum..

UNPLUG YOUR DRYER BEFORE STARTING ANY REPAIRS
I am not sure what plastic part you have, but there should be no small plastic parts in your dryer drum or at least not the ones I have worked on before.
Your problem sounds like drum rollers have flat spots on them or in need of lubrication.
If you have a front loading machine,
Remove the electrical box that holds the timer switch, start switch, etc. from the top of the dryer. Be real careful not to knock any of the wires off of the timer switch. Then remove the top of the dryer.
Remove the front of the dryer. This will expose the drum and belt, remove the drum and belt and this will expose the drum rollers.
Check your rollers for flat spots, if they have flat spots on them replace them.
If they don't then they probably only need lubrication. Lubricate the shaft of the rollers with a good grade of machine oil such as 3 in One oil. Reassemble the dryer, plug back in. This should solve your noise problem.
I will include these two websites for parts and further help:
http://www.partselect.com/
http://www.appliancepartspros.com/index.aspx
Both also have chat assistance 24/7.
Good Luck,
I hope this helps