Hello, and welcome to the Parrot Forums family.
Since predators tend to target weaker individuals from flocks/herds/packs etc, birds as prey animals instinctively try their best to hide their illnesses. So by the time their lethargy becomes easily visible to you, chances are it has evolved into something serious. Now, if this has been happening for the past few weeks, she's probably very sick indeed.
Being on one foot all the time is not necessarily a sign that something is wrong with her foot. (Unless it's always the same foot.) That's how they sleep. But the fact that she's always puffed up is a problem. Puffing up like that is an attempt to hold in as much heat as they can.
Moving her tail up and down when she breathes could be a sign that she is having difficulty breathing. Or that she's straining. Has there been any change in her poop? Take a look at this thread for an idea what I'm talking about in terms of her droppings part way down the page):
http://www.parrotforums.com/general-health-care/48146-photo-informative-collages.html
Egg-binding could also be a possibility with the straining, but I'm leaning away from that since you say she's been this way for the past few weeks.
Yes, you should probably send in a pic of her beak. But your first priority should be to keep trying to find a vet. In all likelihood, her situation has progressed beyond what anyone here could help with remotely. She might be in a critical stage here, and time is of the essence.
In the meantime, you should endeavor to keep her room very warm. 85 degrees Fahrenheit might be good. And watch her eating. Has her appetite diminished? Is she drinking any water?
But I can't stress enough that you need to try your best to find a vet! It's likely the difference between her life and death at this point. Is there a pet store nearby? They may have a vet that they can recommend. Also, we are an international community here. Give us an idea of what city and country you live in. There is always the chance that someone from your area might know of a local certified avian vet. (Or failing that,
any vet. Avian or otherwise.)
I'm really hoping you're able to get some help for your budgie.