On its surface, The Japanese Quince is the short story of a man who is briefly unsettled in his personal life. Mr. Nilson's life is one of routine and habit, and he has little connection with either nature, or with other people. His confusion when confronted with an unfamiliar face, that of his own neighbor, is echoed and reflected back on him.
The "emptiness" in his chest, described as "just below the fifth rib," is easily explained as an emotional need, a distance from substantive relationships. Nilson does not even recognize his neighbor when standing across from him, until he thinks about it; his emotional connections are lacking and so there is an unfulfilled "ache" in his heart, figuratively speaking.
The "sweetish sensation in the back of his throat," the symptoms of which progress to a "choking" at the end, are more likely psychosomatic; the spring morning is full of scents, and some or all of those can combine to trigger taste-buds; however, when coupled with his emotional need, the strange taste seems stronger and more important than it would otherwise.
However, both these symptoms could also be signs of physical ailments; Nilson's aching heart could be a sign of muscular weakness, brought on by lack of exercise, and the sweetness in his throat could be a glucose imbalance, possibly from diabetes. In either the literal or figurative sense, there is something wrong with Nilson's health.