Thank you for getting back to me. I can tell that you care about your turtles, and want to take good care of them, but someone (probably pet store personnel, as that is common) has given you bad information on how to do that. If you want your turtles to be healthy and live long lives, there are some important changes you'll need to make. I'll give you a basic summary of slider turtle care, and then we'll talk some more about Homer, who will need to be seen by a vet.
It's recommended that a one adult slider have at least a 60 gallon tank. Multiple turtles need even more room. If you can't afford a larger tank, you can use the big Rubbermaid totes. It's also possible to find used tanks for reasonable prices in the classified ads and on Craigslist. You want the water to be at least twice as deep as the turtle is long. If the turtle is two inches long, you'll want four inches of water.
Turtles need certain types of lighting and need to be warm. Air and water that are not warm enough can lead to fungal and respiratory infections. Turtles must have a basking area where they can get out of the water, dry off, and bask in very warm light. The ambient air temperature in the tank should be around 75*F degrees, with the basking area warmer still. Over the basking area there should be some sort of lamp that will take a 40-60 watt incandescent bulb (or you can buy a ceramic light fixture made just for reptiles). If you live in an area that has farm stores, you can buy a metal light fixture made to keep baby chicks warm for just a few dollars. Don't buy the accompanying bulb, however. You need an ordinary incandescent bulb in the basking light. Similar metal clamp-on fixtures are sold in hardware stores as work lights. The basking area should be kept at 85-90 degrees. Especially while Homer is ill, keeping it at 90*F is better. Use a thermometer to be sure. You can adjust the temperature by raising or lowering the light fixture. The lights that come with the covers on aquariums are not suitable for turtles. It would be a good idea to get a submersible aquarium heater that will keep the water 78-82 degrees .
It's extremely important that you buy an additional light that produces UVB rays. A Reptisun 10.0 is a good brand that does. If you choose another brand be absolutely certain it provides UVB rays. Don't take the word of pet store personnel, but read it for yourself. Full-spectrum is not the same thing. UV is not the same thing. I'm putting a lot of emphasis on this because it's crucial to your turtles' health. Without this light, Metabolic Bone Disease (MBD) will develop because your turtles won't be able to produce vitamin D. Vitamin supplements are not a good replacement for the proper lighting. MBD causes a very slow and painful death. Your tutrles probably are already in the beginning stages, but it can take years before the disease kills. UVB bulbs must be replaced every six months as they lose their effectiveness after that, even though they may still look fine. Light that comes through a window isn't sufficient because the glass filters out most of the rays turtles need to stay healthy.
Turtles are very sensitive to water quality. Even if you change the water every day, it can still contain harmful chemicals. A good filtration system is essential. Water changes are also needed even with a filter. If you don't already have a filter, consider getting a good one. Unfiltered water often leads to bacterial infections.
Feeding is another area where pet stores often give out bad information. Commercial food should make up 1/4 of the diet. Animal products (meat, earthworms, canned cat food) should make up another 1/4. The remaining half should be plant foods (dark lettuce like romaine, bits of strawberry or melon, etc.)
You may want to look at these sites for additional information on care and feeding. I especially recommend that you check out the lists of appropriate foods.
I would recommend that you provide the conditions your turtles needs as soon as possible. Without those conditions, turtles are likely to die, no matter what pet store personnel may have told you.
Homer most likely has a bacterial infection. A nutritional deficiency could also be the cause. It's even possible that he has both a deficiency and an infection. There are many causes of swollen eyes besides vitamin A deficiency. Too much vitamin A can cause health problems, so I don't recommend that you supplement without seeing a vet. Bacterial infections can quickly turn fatal in turtles, so the sooner you can see a vet, the better. If you need help finding a reptile vet, give me your city (nearest larger town if yours is a small one) and state, and I can help.
If you have further questions, just let me know by clicking on REPLY. I hope Homer will reach a full recovery.
(If you find my answer helpful, please click on ACCEPT. Thank you.)