How old is she? Many things can cause limping, but my first guess is that she has Marek's Disease. This is based off the first symptom being limping and that then transitioning to a stiffer leg and balancing using a wing. These are common symptoms for Marek's Disease.
Marek's is a viral disease in chickens that primarily affects relatively young birds (usually 6-10 months old) but can affect older birds or younger ones. It causes, in many cases, steady paralysis beginning with the legs and often affecting wings. It can also cause deformed pupils in the eyes, internal tumors, and feather tumors. Many birds that come from a hatchery or feed store are vaccinated for Marek's Disease as young chicks. The vaccine isn't 100% effective (more like 90-95%) but it is a good preventative measure. However, not all chickens are vaccinated and even the vaccinated ones can succumb to the disease. Marek's Disease is extremely prevalent. It survives for a while in the soil, is hard to kill, and is spread through feather dander. Many people believe that if you have chickens, you most likely have Marek's on your property already. Some breeds and individuals are resistant to Marek's and people may never know they have it (especially if they have vaccinated birds, which usually show no symptoms). For example, Cochins and Japanese Bantams are resistant while Silkies and Dutch Bantams tend to be very susceptible.
If it is Marek's Disease, there isn't much you can do. Some people have had success with herbal treatments like St. Johns Wort so you could look into that (here's a good link: St. John's Wort). Some birds "recover" from Marek's only to have the symptoms reappear.
While I believe Marek's to be the most likely problem in this case, it could be a vitamin deficiency. This can cause neurological problems such as odd wing carriage or limping. You could get a poultry vitamin (like Nutri-drench) from your local feed store or poly-vi-sol infant vitamins (without iron) from a supermarket and try giving her some of those. If it is Marek's Disease, the extra nutrients may help.
It could also be an injury, but if her leg is becoming stiffer, I don't believe that is the case.Injuries can take a long time to heal. Keep her well rested (no jumping from high roosts or onto hard ground) and provide good nutrition.
Diseases and disorders with these symptoms can be hard to diagnose. There's no way to know for sure whether its a sprain, first sign of Marek's, or a vitamin deficiency so I'd just treat with vitamins and rest. If it is Marek's, it will likely get worse. If it is a sprain or strain, it should get better but it may take a while.
For more information on Marek's Disease, I suggest looking at this very informative article: The Great Big Giant Marek's Disease FAQ
Best regards to you and your bird and I hope she gets better!
Edited by Wyandottes7 - 11/6/15 at 2:53pm