Sounds exactly like my little Thalia! She kept her eye closed all the time, and it eventually got really swollen. I found out she had an eye infection and imedietly started treating her with saline and coconut oil. I used 1/8 of a teaspoon to one cup of water and put a few drops in her eye, then I rubbed a little coconut oil on it with a cotten swab, both twice a day until the swelling went down and she was keeping her eye open. She has a blind eye now, but at least the infection didn't spread and kill her.
She was also really small, wasn't getting any feathers, and it didn't seem like she was growing. She was always acting like she was cold and getting pushed around by the others, so I put her in a separate brooder with one of the sweeter chicks, and kept the temperature higher. I gave her a few drops of straight nutri drench and straight coconut oil in her beak twice a day with a dropper, until she was 4 weeks old. I also used electrolytes, probiotics, and 2 teaspoons to 1 quart of water of apple cider vinegar. I also gave her extra snacks. I made this super nutritious chick mash that the chicks love! I made scrambled eggs cooked in coconut oil mixed with a little bit of starter food, chick grit, plain organic yogurt, and topped it with crushed meal worms. I almost wanted to eat it! I also gave her chick baby cake, and mixed chick kibble with her food. She is now 5 weeks old today, and has grown some and has some feathers now. She is still smaller than the others, but she's starting to catch up. She still has a heat lamp, but hopefully she won't need it much longer (I'm gradually lowering the temperature based on her feather growth rate.) I'm now alternating between the electrolytes and probiotics, and nutri drench in her water, and keeping up on the snacks. This is how she looks now: