First, thank you to Joan for passing on excellent information. An infection that causes the legs to swell is usually pretty severe. The steps that Joan recommended need to be taken - providing the proper conditions and seeing a vet. I suspect that you got your information on turtle care at the same place you purchased them. Unfortunately, that information is usually incorrect, and many turtles die because of it. I can tell that you care about your turtles, and want to do what's best for them. Since you want your turtles to remain alive and healthy, there are some important changes you'll need to make.
Turtles don't get sick immediately when conditions aren't right. Their bodies do the best they can, but something finally tips them in the direction of illness. The stress of the move could have been that final straw, but it isn't the cause of the illness. I'll give you a summary of the proper conditions you'll need to provide, but you can get more details at the site Joan recommended above.
Turtles need certain types of lighting and need to be warm. Air and water that are not warm enough can lead to 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 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. The basking area should be kept at 85-90 degrees. Use a thermometer to be sure. You can adjust the temperature by raising or lowering the light fixture. Since your tank is small, set up the basking area at one end - you don't want the entire tank to become too warm. A lack of a basking area also leads to various infections. The lights that come with the covers on ten gallon aquariums are not suitable for turtles. You'll also need a submersible aquarium heater that will keep the water 78-82 degrees.
It's extremely important that you buy an additional light that produces UVA/UVB rays. Make sure it provides both UVA and UVB rays. Don't take the word of pet store personnel, but read the label for yourself. Full-spectrum 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. UVA/UVB bulbs must be replaced every six months as they lose their effectiveness after that, even though they may still look fine.
You will want to get a bigger tank as soon as you can. If you watch the newspaper classified ads, local shoppers, and perhaps CraigsList, you can often find used aquarium tanks for reasonable prices.
Turtles are very sensitive to water quality. Even if you change the water every day and it looks clean, it can still contain harmful chemicals. A good filtration system is essential. Water changes are also needed even with a filter.
Feeding is another area where pet stores often give out bad information. Commercial food should only make up 1/4 of the diet. Animal products (meat, earthworms, canned cat food) should make up another 1/4. While you're correct that iceberg lettuce isn't good for turtles, they really do need some plant foods. As Joan stated, plant foods should make up half of their diet. The following site has a good list of appropriate foods.
I would recommend that you provide the conditions your turtles need as soon as possible. Without those conditions, your turtles are likely to die, no matter what pet store personnel may have told you. It's extremely important that you take your turtles to a reptile vet as soon as possible to begin treating the infection.
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