I'll give you some links below.
If she is eggbound you can often feel the egg near the vent, through the skin. You can also put your finger up there a short distance to check.
If she had cocci, she most likely would be refusing to eat or drink. Also, they usually sort of sit hunched over as if they were cold. Cocci most often gets young chicks sick; usually by this age, they have developed an immunity, unless they were exposed to a new strain (cocci is a protozoa that lives in the soil, and there are 9 strains that affect chickens.) You could try a round of Corid for cocci if you wish; it is a relatively harmless drug for the chicken, which interferes with the cocci's ability to take up thiamine, a vitamin. You should be able to buy Corid in your feed store.
I would probably try treating her for worms. If they have a heavy load of worms, they can certainly lose weight, as the worms eat a quantity of the feed before the chicken gets the benefit. Valbazen is the only drug that gets all worms that chickens get. The dose is 0.5 ml by mouth (put it on a scrap of bread or squirt it in the side of her mouth), repeat in 10 days, toss egggs for 21 days. It's a cattle wormer, available from Jefferslivestock.com or
Amazon if your feed store doesn't carry it. The smallest size unfortunately is 500 ml, about $40. If conditions are warm and wet wher you live, as they are here, you should probably worm your flock once or twice a year. Soil is really wormy around here, and some experienced people worm as often as 5 times a year. If she happens to have tapeworms, fairly unusual, the dose is higher. If she does, you should see the segments in the poop. (see link.) The first time I wormed my flock, I could see that they gained some weight after, and yet they started eating less feed.
I'd also try some some probiotics; again, they can't hurt. A tsp. of yogurt once a day for a few days will do this, or a bit of buttermilk, or some human probiotics if you happen to have some.
http://thecozynest.com/understanding_coccidiosis.htm
https://www.backyardchickens.com/t/775739/blood-in-older-chicks-stool/0_20#post_11087272
https://www.backyardchickens.com/t/...ll-seeing-live-worms-in-poo/0_20#post_9315842
http://healthybirds.umd.edu/Disease/Deworming Birds.pdf
https://www.backyardchickens.com/t/...peworm-or-any-worms-really/0_20#post_11670181 (see esp. post #7 on tapes)