She's breathing ok. She only had to stop that once in the pasture to cough that stuff out. Mine didn't have that strangling sound and problems breathing when they had stangles because they ruptured but they would have to stop and cough junk out with any exerction including walking. If it's a relapse it's very mild or she's in the early stages.
I wouldn't keep strangles out of the picture, and I'm inclined to think that it might be, but I also don't want to get you all worried in case I'm wrong. (And I also realize that a few posts ago I said it might be an infected wound, but I didn't realize that she was coughing stuff up) Either way I think it's important to test for Strangles right away because of all the other horses. How long has this been going on?