I remember that episode well. Hawkeye recalls being on a bus where everyone has to be quiet to avoid detection but a woman has to silence a chicken and has to kill it to do so. But it's a false memory and it wasn't a chicken it was actually the woman's baby that was crying and was killed by its mother. This triggers a memory in Hawkeye when he was younger and someone (his brother, relative or best friend - some one he admires anyway) is meant to have rescued him after he fell into water - but again the memory is false and his hero hadn't been trying to rescue him but had actually held him under the water. The 'case is solved' when Hawkeye lets slip that he puller under the water and not out of it.
I can't help with locating the episode but maybe that fuller description will help some one else locate it.