First off, welcome to the Forum.
Can you post some pictures of your setup?
Presumably they are in the same tank? You say the RES is a weak swimmer - why? The recomended requirement is 40 litres of water per inch of shell for the first turtle and 20 litres per inch for the second so they need way more water so that they can both actually swim.
Without photos we cannot say if they are overweight although you are feeding a protein rich diet - how often and how much do you feed? What are the floating sticks you are feeding?
What age/size are the turtles and do you know their sex? If one is male and the other female then that could be a problem, together with two males may not get on.
Again, heated water is not necessary for adult turtles, but we need to know their age. You cannot just guess the water temperature!
What is the temperature of the basking area? Is there a lid on the tank? I am wondering from what you have described if this is the start of a respiratory infection especially in view of the "noise". In which case, and if they are together, they will both need antibiotics and veterinary treatment. It is contagious and needs treating.
You may want to repost in the main Shelled section, where more people will hopefully look and respond.
Are you in the UK?
Sorry for all the questions, but we need as much information as possible from you before we can really begin to help.