Uhm, there are a lot of things that can cause a chicken at 1 year of age to go off lethargic and by itself other than egg binding or egg tract issues.
Was she standing in a penguin position? Can you/did you feel an egg in the tract that had not passed? Those are the usual symptoms of egg binding.
Simply not laying for a period could be molting (are feathers floating around or do you see pincushion pin feathers?)
Is there any chance she is trying to go broody? Is her lethargy in the nest box, or off to a corner in the run. Is she standing or sitting, in a nesting position, while she is there?
Are there any other signs? Diarrhea, runny nose, wheezing?
Is she unthrifty? (Losing weight, not eating or drinking, rumpled appearance)?
Often when a bird is lethargic it can be internal worms or coccida lurking. Did your vet do a fecal test on her poop to rule that out?
You can try a force molt, but I'm not convinced that is the issue unless you know for certain, and it was verified by an experienced avian vet, that her problem is egg binding or egg tract infection (for which she would need antibiotics as well).
To force a molt, the chicken industry usually refrains from feeding the birds for 5 to 14 days (a practice coming under condemnation). Modified methods are an elimination of lighting with modified feed (removal of calcium).
A hen's pituitary needs 12 hours of daylight to begin to release hormones. It needs 14 hours of sustained light to lay well. We are at that now with the summer day lengths (if you are in the Northern hemisphere).
You could put her in a cooler area with dim lighting for a week on lighter, non-layer feed to see if that works. You might see a forced molt then, or not, as I don't think you really want to do the whole 5 to 14 days on no/low feed in a dark room....and again, I'm not convinced that is her problem without further information from the information you've given.
Did the vet give you his/her reasons for thinking it was the egg tract?
My thoughts,
LofMc