Yes, she could be egg bound, among other things. You can check for egg bound by lubricating a finger and sticking it in her vent, or you can just proceed with treatment without checking. Soak her lower half in warm (90-95 degree F.) water for a while, and then take her out and dry her the best you can with a towel. Isolate her in a clean, darkened place and give extra calcium (in the form of oyster shell, crushed egg shell, human calcium pill, etc.). In most cases, these measures will cause a hen to pass a stuck egg.
Another possibility is that she has the beginnings of vent gleet, a fungal infection. Here is a link on the topic:
https://www.backyardchickens.com/a/vent-gleet-aka-nasty-chicken-butt Or, she could have some sort of digestive problem. Green droppings are common in birds that aren't eating enough. Worms are something to consider, too. I would purchase a good wormer (some choices include Valbazen, SafeGuard, or the Worminator) and worm her, just in case. Also, check her crop in the morning, at which time it should be empty. If it is large and hard, she may have impacted crop. And if it is large and squishy, with a sour smell coming from her mouth, it is likely that she has sour crop.
Other things to check for include external parasites (mites, lice, etc.), respiratory disease signs (nasal discharge, sneezing, etc.), swelling anywhere on the body, injury, and how much she weighs (does she seem light?). Also, how old is she, and what are you feeding your hens? The more information you can provide about her symptoms and care, the easier it will be to diagnose her problem.