Me duele el pecho pero me lo echo
 

Just now heard this, I believe in the context of someone at the dinner table who wants to apologize for taking the last remaining item of food or drink. Right?

Never heard it before, but it could suit the context.

In Mexican slang, "echarse algo" can certainly mean to eat/drink it. :)

· Vamos a echarnos unas chelas, ¿no?
Let's have some beers.

· De camino a la casa me eché unos tacos.
I ate some tacos when I was coming home.

In Chile, more or less the same.

Me duele el pecho (en el alma) pero me lo echo (al pecho)

It is going to hurt me, but I'll take it anyway. :)