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.
My rooster had a limp. I couldn't detect any sore spots or bumblefoot, but I rinsed his feet off in water and sprayed them down good with Blue-Kote. I saw a noticeable improvement within two days. He still has a tiny limp, so I plan on spraying one more time. It is both an antifungal and anti-bacterial. But the iodine stains everything purple like a son of a gun, so wear rubber gloves if you apply it.
They sell it at Tractor Supply (back by the goat and horse meds) and Amazon. I use the squirt bottle kind. It is good to keep on hand. I use it on my dogs too--but I keep them outside until it dries. It can seriously stain carpet and fabric.
My EE just started limping today at 32 wks. Laying fine. Not a problem. Gave her an epsom salt bath (which she didn't like). Doesn't look like bumble foot either. Alert..will eat though I think she may have a little diarrhea, but not sure on that. She can fly just fine...not unsteady. Here's my question about isolating her in a cage. Should I put the cage (it's a large dog crate) inside the coop's run to keep her around the chickens or bring her inside during the day? Nighttime I'd probably bring her in so she doesn't get cold sleeping by herself. What do you think? Also, what do you think about the idea of giving her half of a low-dose chewable aspirin for pain?