A photo would be useful, and I have no idea how to post them myself!
Egg-bound is when the egg is stuck in the oviduct and then hen can't lay it. Most often, when people notice this, it's because their hen is walking funny - waddling in an upright, penguin-ish posture, sometimes appearing to be straining. Hens can die if the egg does not come out, so a quick exam is a good idea. If she is egg-bound, you can often feel the egg if you lightly palpate her abdomen/hind end. Be careful not to break the egg, as that can kill her. A good way to get a hen to expel a stuck egg is to soak her in a tub of warm water. Her muscles will relax and release the egg (a banty of mine that was eggbound released two eggs). Eggbinding usually occurs in older laying hens. Having oystershell available for your hens is a good preventative, but it isn't a guarantee.
There is a very informative thread here somewhere about eggbinding / being egg-bound with lots of specific tips, and if you think this may be her problem, you'll want to check it out.
When you catch her, give her a once-over. Check her feathered feet for scaly-leg mite (the scales on the legs/feet will be white and crusty and pushed up), check the bottoms of the feet for bumblefoot. Heavy breeds like Standard Cochins (I have a splash one myself) can get bumblefoot (a staph infection in the foot pad) and not show signs until the infection's well underway. If she's got bumblefoot, you'll know as soon as you look at the bottom of her feet (which may be very warm from infection). You'll usually see a swollen foot pad and a nasty black scab. Under that scab is an infected core that will have to be removed.
The thread on bumblefoot has tons of info on this, and probably some gross photos.
Scaly leg mites are another possibility, if her feet are heavily infested with the mites and their function is impaired. There are a variety of things you can give her or slather on her feet/legs to kill the mites. I think there's a thread here for that soo, since it is a common problem.
Another thing it could be is an injury. Just like us, they can be clumsy and fall off stuff, or get stuck in a tight area and wrench something getting out. I had a huge buff Orpington cockerel who spent the night wedged between our two oil tanks: legs down, wings up. I heard his pitiful croaks in the morning & released him. He had spent a rainy night just stuck in there and was just miserable. A few days later he was back to his old stuff.
Much of the time, you can judge the seriousness of a chicken illness or injury by seeing what they do. If your girl is walking funny but otherwise acts like herself, if her crop is full and she is free from mites and bumblefoot and doesn't appear eggbound, I'd say just keep an eye on her. Check her out first, and if she looks okay, just monitor her for awhile & see if anything changes.
You'd be surprised how well chickens can behave in the bath. I've washed many a chicken, and only my Jersey Giant ever tried to fight her way out of the tub. Sometimes you have to just hold them for a few seconds first, until they know they can't move but are not falling to the ground. Lower into the waiting water - you may need to put your hand on her back for awhile, gently, once she's in the water. It may take 30 seconds or so, but they usually relax after that, sometimes even drooping their wings open or drinking the bathwater. Or they may stand there stock still for awhile longer.
The bugs sound like fowl lice (aka chicken lice) to me. They are kind of creamy/pale yellowy & they crawl all over. Their egg cases are often seen at the base of the feathers on the neck, in the beard / muffs , and they look like little clusters of salt around the base of the feather. Lice are a nuisance, but pretty easy to get rid of. As a matter of fact, I'm dosing my chickens tomorrow for chicken lice with ivomectin (injectible); there is also ivomec eprinex (it's dropped on the skin), and I'm sure there are organic and other remedies out there, too. Unlike cat and dog fleas, the lice cannot live on people (or dogs and cats) and are only a nuisance to chickens (a major infestation might cause chickens to be weak & thus susceptible to other ailments). I think the ivomectin / ivomec eprinex works for a few months, and it also kills scaley leg mite (leaves legs and toes whitish, dry and scaley). There's probably a thread here on lice remedies, and I think there's some on ivomec. Hope this helps!