redeared slider mouth open

Question
turtle keeps stretching out his neck and opening his mouth, like he has something caught in his throat. Not eating.

Answer
There are a lot of possibilities here, from something called ulcrative stomatitus to several viral diseases to some simple care problems like cold water.

Not being a vet and not having any information from you about size, habitat, diet, etc. I cannot really make a good guess.

You might try the forums at http://www.turtleforum.com and see if the people there can help. At least in the forum you can give answers and get advice in a more rapid way than we can do here.