According to the Japanese Wikipedia, "himehajime" can be interpreted in many ways, but all of them refer to different rites of passage which a girl might go through on New Year's: the first time she does housework, the first time she rides a horse, or (ahem) other "first times".

I think there's no question as to which of these Elza is thinking of. The final panel is almost certainly a fabrication though.

I always thought it was the 'scream' or 'cry' reading of hime used in himehajime, as in a screaming start. Would definitely erm...fit the context