Anton Chekhov's short story "Misery" has a subtitle "to whom shall I tell my grief?" Discuss the significance of the two titles and how they relate to each other.

Clearly, the title and subtitles complement one another. The title "Misery" refers not just to the main situation of the story, but also to the overall mood of the tale in itself. 
Our main character, Iona, is an old cabman who is poor, tired, has an old mare as his working animal, and is currently suffering the worst pain any human being can undergo: he is grieving the death of his only son. 
The entire situation is miserable as it is. The man lives in dire conditions, works under dire circumstances at his old age, and endures the abuse of bad patrons that neither pay well nor treat him with any degree of decency.
The poor man is so used to the abuse, and so far gone in his own pain, that he does not even have the capacity to differentiate the abuse that he suffers. All he wants to do is tell someone about the death of his son.
Like any human, he wishes to let his thoughts out; to properly put an end to that chapter of his life. He wants to express his emotions, explain how it all happened, and render some sort of homage to his child, even if it is in conversation. Nobody listens to him. Here is where the second title, "To Whom Shall I tell my Grief," comes in.
Iona is a widower, and his daughter is somewhere in the country. Being that these are the days prior to any type of electronic communication or social media interaction, you may be able to picture the extreme degree of loneliness that this man must be feeling, alone in the world, and with nobody to talk to. The man tries to tell his pain to the military officer that he first drives. He then tries to tell the rowdy youngsters who needed his services and ended up abusing him. He tried to tell someone at the place where he lives, but that person just turned around and kept sleeping.
In the end, there was no other choice but to go straight to the mare, and speak to it. The animal, who was eating hay at the time, simply continued to chew as the man was finally able to say what he had to say. 

"That's how it is, old girl.... Kuzma Ionitch is gone.... He said good-by to me.... He went and died for no reason.... Now, suppose you had a little colt, and you were own mother to that little colt. ... And all at once that same little colt went and died.... You'd be sorry, wouldn't you?..."

Therefore, the story reads as a critique of society and the narcissistic and selfish ways of people who look down on others; people with no empathy or humanity who rest importance to the vicissitudes of a fellow man. That an animal ended up being the only one listening to Iona's sad tale speaks volumes of the type of society that Chekov based his story upon.