"Go suck an egg" is a saying typically used similarly to "take a hike" or "piss off": Hey, you going to help me with this or what? Go suck an egg. An few Ngram searches shows that "suck an egg" is only really used with the words "go" and "an" but I was not able to .
Go suck an egg unknown Phrase finder suggests that the saying originates from the dictionary definition of the term "suck-egg" which refers to: An animal that is reputed to suck eggs, e.g. a weasel; figuratively. an avaricious person. It is also considered to be a dismissive insult similar to the term fuck off but is less abrasive.
If someone tells you to go suck an egg, they are telling you in a rude way to go away. If she criticizes you again, just tell her to go suck an egg.