Hello -- I own three celadon coturnix quail (two males, one female) as pets. All of them are three and a half months old and are separated to prevent biting. The female began laying around mid-December. She lays one egg everyday aside from occasionally skipped days. However, she makes a cry-call after laying an egg, and I find it concerning. She suddenly appears skinnier (less fluffed), has more difficulty to move her body and head around, closes her eyes, and becomes increasingly sensitive to background noise. I feed her three to four mealworms to replenish her calcium levels and "sleep" (close my eyes) with her to help her feel safe. This call continues for around twenty to thirty minutes while she sits on her alfalfa bed. After this time passes, she is able to eat, drink, pass feces, walk, fly, do what quail do, and seems healthy. It is just during the time she cries that is very sad and worrisome. From researching online the crying is said to be a normal process, either to alert any male quail nearby or similar to a way of saying, "Everybody, I laid an egg!" However, I can't help but still feel she does feel pain. If anyone has additional information, such as ways I could help her, please do feel free to leave a comment. Thank you for taking the time out of your day to read my post. 
Youtube videos featuring similar cry-calls:

Youtube videos featuring similar cry-calls: