Hi chooks4life..thanks for the response..this is driving me crazy. The answer is I don't think so but it certainly is possible. I also am leaning towards injury but I just wanted more feedback because of the timing. Also there had been no improvement and I am getting worried about the prospect of this being a permanent condition. I don't have much experience with chickens. Can a chicken live a happy life like this?
Both Ivermectin poisoning and injury are definitely possible, injury probably more so since chooks overall seem to have a higher tolerance for Ivermectin than dogs, cats etc...
If you can get a photo, or several, or a video, it will almost certainly help; sometimes it takes experience to spot an injury.
The part where you said it is dangling and getting bent makes me think it's more likely an injury since if it were paralyzed it'd end up most likely straight out, dragging, behind it.
The paralysis or weakness, whatever it's caused by, is unlikely to stay in stasis --- it will either get better or worse, and generally quite quickly too. Because chickens are bipedal, when they lose use of one leg it is a serious issue, unlike a four legged animal their chances are much poorer. Conversely the broken bones of chooks tend to heal very well, but time is of the essence.
Some birds will get along on one foot just fine but many others end up injuring their healthy leg in overcompensation for the weak one, and rapidly you find you are dealing with two injured legs instead of one. Can be very hard to fix, even impossible, and a fix can take months of daily physical rehabilitation.
It all depends what's wrong. Finding that out is most important. It may be a torn or strained tendon or muscle or joint cartilage, or a broken or dislocated bone, or paralysis due to toxicity or nerve damage.
The first lot of hatchery chooks I bought actually had a hen who arrived in terrible distress with her leg straight out behind her. She died that day and we cut into the joint to see what happened, and found they had torn her femur head straight out of the socket when they caught her with the wire. They, like many, used a hooked wire; it's very dangerous whether it's ripping the internal structure of the legs or stabbing them an inch deep into the abdomen with the dirty wire hook point when they miss a leg. They told us, prior to her death, that it was a 'cramp' and suggested we massage her leg. When she died and we told them what we found, they hung up on us rather than offer a refund; they chose preservation of a few dollars over reputation, lol.
Anyway, by their reaction we knew this was not uncommon. Back on topic: I would get or make a little cage for her, where she can sit with food and water in immediate reach so she does not need to get up to feed or drink, with mesh walls so she and her flockmates can see one another but she can't be picked on and won't feel lonely; I would confine her in there, making sure her leg is in its correct position under her, and give her at least 2 days to see how it goes.
'Walkable' healing can take only a few days, though the true knitting of the bones will take several weeks or months; tendons generally take longer than a few days if torn but can rapidly heal if only strained; a damaged joint could take any amount of time; a dislocation will require immediate intervention to fix; toxicity related paralysis should be showing other symptoms too... It's too complicated to offer a best course of action suggestion when we don't know exactly what is wrong.
Best wishes.
