That sounds like lice eggs. They are more an indication that your hen is unwell rather than the cause of it. A sick hen will not preen and dust bath enough to remove these parasites. There will usually be a low level of lice in a flock which they should be able to manage themselves unless the ground is frozen solid or very wet and dust bathing is not possible. Providing a dry dust bathing area for your flock if natural opportunities are not available is good practice, but if a hen is sick then she will struggle to keep on top of them and may reinfest the others more quickly. It might be worth dusting/spraying her and the others and the coop with permethrin to get back on top of things.
It is difficult to assess the swelling from the photos but her legs do look quite wide apart. Does it feel like she could be full of water.... the rumbling noise might suggest that. Do you feel able to stick a needle into her belly to try to drain her. The draining needs to be done quite slowly so that her body doesn't go into shock with the drop in pressure. A vet is probably the best bet if you are not confident. If you decide to try it yourself, there are video tutorials on You Tube. Ensure that you cleanse the area well first so that you do not introduce infection into the abdominal cavity
It is difficult to assess the swelling from the photos but her legs do look quite wide apart. Does it feel like she could be full of water.... the rumbling noise might suggest that. Do you feel able to stick a needle into her belly to try to drain her. The draining needs to be done quite slowly so that her body doesn't go into shock with the drop in pressure. A vet is probably the best bet if you are not confident. If you decide to try it yourself, there are video tutorials on You Tube. Ensure that you cleanse the area well first so that you do not introduce infection into the abdominal cavity