Megan, thank you for your honest answers. The good news is that you care and want to help this hen - thank you. Have you named her?
As Diana noted, it's imperative that she get on a better diet immediately, if not sooner. In addition to the layer food, hurry if you can to order some Avia Charge 2000 (you can find it on line), a nutritional supplement that gets added to her water. She has lots of nutrition to catch up on. A little goes a long way and the jar will last a long time.
The feed store should be ashamed that they gave out wrong info about diet - the same thing happened to me many years ago when 2 roos appeared on my property out of nowhere (I had never had chickens before so I didn't know and the feed store told me in no uncertain terms that a roo diet is scratch and only scratch) - once I got the straight story (scratch should only be used as a treat, not as prime diet) I had a talk with them and every time I hear one of their employees give out wrong info yet again I correct them. Feed stores that give out wrong info like this are condemning birds to illness and early death and that's akin to a crime in my book.
Being caged up small, with no feathered friends, humans that don't have enough time to spend with her free of cage, a diet that is nutritionally inferior - it's not surprising that she's unwell. It's been a half a year already. Her best chance is if you hurry to make changes for her - hurry like it's an all out emergency.
I only have 2 (a roo and hen) but they are bored in a nanosecond if they are not out and about exploring (even though they have a 4'x6'x8' high coop for sleeping in a 24'x24' outbuilding they have the run of in the daytime). Perhaps you can think about getting her a friend (if you do, check back with folks on BYC and you can get info on best way to introduce etc.) or at least finding a way to offer her more exploring time. If neither of these things is possible, her best life might be with someone else who can reliably offer these things (that takes some careful investigating!).
Examples of dietary supplements that you can offer in addition to layer food (layer should be the main thing, these others as treats): sunflower seeds (mine get them every single day for umpteen years now - in the shell), scrambled egg (scramble an egg in a ceramic cup, mixing in one tablespoon water, and microwave for maybe 30 or 45 seconds, mix well and serve after no longer hot - this can be offered for extra protein during molting or when needing to entice them to eat for whatever reason), small cut up pieces of fruit and veggies (mine love tomatoes, grapes, melon, berries, apples, bananas and so on.....), always making sure the condition of these foods is something you would eat yourself (no mold). Fresh plain yogurt. A teaspoon of apple cider vinegar (with the mother) - get at health food store - per gallon of water offered once a month in plastic not metal water bowl. Dosage recs vary on ACV - one teaspoon is on the low side. Don;t use Avia Charge 2000 on the day you use ACV.
Okay, late for work now but I wanted to spend some time seeing if I could help you help her. Sending best wishes. Please keep us posted - you're on your way to better health for her!
JJ
