Puzzled

I was guessing a seed also till you said the swelling started at her elbow. A seed probably will not show on an x ray however a broken toe will. Broke toe isn't any biggy unless an infection sets in the bone. Splintered toenail that's went to the quick might get infection too. If yall can't find the answere and it seems to be something that's not going away, i would get off kibble and put the dog on a raw diet. Just because a dog has been feed kibble all its life for 4 years doesn't mean it won't develop an allergy to the cereals in it. Cronic inflamed nail beds, unexplained hair loss, sores that won't heal etc will often time clear up when switching a dog from kibble to a proper raw diet. Their body can fight infection better and wounds heal quicker. Not saying it's her diet but when puzzled, it's a good place to start trouble shooting when antibiotics aren't getting rid of something for good. I'm sure you know as well as anybody that it's not good for a foot with a problem of sorts to be allowed to step in urine and feces. So wrapping the foot seems like a good idea but it can often make such a problem worse, especially when the toes are not gently seperate when wrapped and wrapped gently and instead of the infection draining, it will keep it in her body and make the problem much worse.
You mention the swelling now has went to the elbow. Is this area hot to the touch as in has a fever? If not, this may be air that's being drawn into the wound when she was feeling better and moving the foot a little. If it's indeed air , it won't be hot with infection and not to big of a deal. Her body will absorb the air in a couple days win it stops drawing in air when she moves her foot if this is the case. I would put a poultice on the effected area for a half hour twice daily that will help draw out the infection or at the minimum treat the area with a local anticeptic cream. Along with general antibiotics.
Very intesting! Hope she gets better soon and you find an actual reason for this!