If I copyright my music..?

I think you can have ownership and actually use it as one of your videos too. If your company receives copyright complaints they will most likely hit dismiss/ignore. 

First you need to explain what you mean by, “if I copyright my music...” - what would that involve?

If it really is “your” music then you automatically own the copyright on it and can do what you like with it.

I've never heard of “distrokid” but, obviously, you need to ensure that you don't (or haven't already) sold or given away your copyright.

It depends on what you agree on. But if you wrote and performed the song then it would be your song unless there us an agreement that the other person now owns it. Contract on paper would be your best bet