Likely not egg binding. Limping is not usually a symptom of it (usually, a penguin like walk, swollen hard abdomen, and lethargy are the symptoms).
Three possible causes that come to mind are bumblefoot, an injury, or Marek's Disease. Do a thorough check of both legs. Check for any bumps, bruises, or signs of pain when touched. Bumblefoot is an infection in the footpad. It causes swelling and often a black scab on the bottom of the foot.
In the early stages of bumblefoot, you can treat by providing antibiotics like Penicillin. However, if it is a severe case, surgery may be needed to extract the infected pus-filled core.
Sometimes, birds sprain or strain their legs by jumping down from a high roost or something similar. You may not notice any external symptoms, other than limping.
If you suspect this, I'd isolate her in a well-bedded place where she can't injure herself. Provide vitamins (you should be able to get some poultry vitamins at a feed store, or online) to help healing. Eventually, leg injuries should heal.
Marek's Disease is a disease common in younger birds, around your bird's age. It often begins as limping, then slowly progresses and paralyzes the bird. Since this came on suddenly, I think that this is perhaps the least likely of the problems. Here is a good link to read on Mareks:
The Great Big Giant Marek's Disease FAQ
One last, but unlikely, thing that could cause limping is a vitamin deficiency. This shouldn't be a problem if you are feeding a complete feed (unless the feed is old). It is more common in younger birds several weeks old.
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Best wishes to you and your hen.