***Not a teacher***
I haven't actually seen this episode of Friends, so I cannot be totally sure, but this is what I would guess from the little context there is....
Chandler saying "I'm very very aware of my tongue..." probably means "I know how often I get my self into trouble by saying stupid or embarrassing things". So if the context in the episode is that people are trying to get Chandler to get up and say something, make a speech or something like that, then this is the most likely meaning. There are other possible meanings though, but I would need to know a bit more about what they are trying to encourage Chandler to do before I could comment on that.
'ego shrapnel' is not a term I have ever heard before, and I assume the writers of Friends have made it up. Shrapnel refers to fragments of a shell or bomb which can cause injury when the bomb explodes. Ego (in very simple terms in this context) is referring to self-esteem. So I assume Ross is saying to everybody "Look everyone, Chandler is going to make an idiot of himself, his self-esteem is going explode (be destroyed) and blown into little pieces (shrapnel)".
As I said earlier, these are only guesses as it is quite difficult to be more sure without more detail of the context.