There are different kinds of tears with different functions. Some for lubricating the eye and some for expelling an irritation. The third group "Emotional tears" are the least understood and their chemical makeup consists of proteins and hormones, some secreted by the pituitary gland. Proteins are made of amino acid chains and when proteins are broken down then ammonia is a byproduct. This could account for the strong ammonia smell of intense emotional tear production.
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You may be eating/metabolizing too much protein. If not, then you should get your blood checked, especially -- liver function tests. It might be nothing or could be something serious. I have been through this myself - notice when eating too much meat; also could be my liver -- have blood tests every three months. Good luck.