Every day he walks on knives.
This is not a perfect analogy. Unlike the mermaid of the tale, he can talk to the one he loves, and he would hardly have made a sacrifice like this in the first place if there were anyone else in the picture. But he's a fish out of water, cast up onto land to gasp and eventually die, and every human activity that seemed so interesting, so different from the tedium of immortality once, has come to be excruciatingly painful.
It was the only way he could get permission to have what he wanted and the only way he could persuade Picard that he was serious about his feelings. He still thinks the man was inherently worthy of the sacrifice. When things are going well, he doesn't regret his decision. Well, mostly not. But every day the mirror shows him another gray hair, a slightly further receded hairline, another wrinkle. Every mission Picard goes on fills him with absolute terror, that this might be the one his lover won't return from. Starfleet is a dangerous business. It's not all that safe for him either, even as a civilian science advisor-- entire starships can be destroyed by enemy fire-- but at least he doesn't ever have to go on dangerous jaunts onto unknown planets or get involved with ridiculous diplomatic charades. Picard does. And someday he might not come back from one.
And that's when things are going well.
Sometimes he looks out at the stars and realizes he will never see them in their true glory again. Sometimes he tries to remember something he should be deeply familiar with, only to find the memory has disintegrated under the pressure of mortality. Sometimes he's bored, and alone, and unlike before there's nowhere he can go and nothing he can do to alleviate the boredom. He can become furiously resentful then, can take it out on Picard for driving him to this, or on anyone who happens to cross his path. Picard usually tries to avoid him when he's like this, which only makes him angrier, but he can't exactly teleport into Picard's ready room anymore. One time he hijacked the transporter to do it, but he was told that if he tried it again he really would end up in the brig, captain's domestic partner or no.
Frequently he hates Picard for driving him to this, for leading him astray so badly, for making him fall into this weak emotion and sacrifice everything for it. Rationally he knows this is unfair; Picard didn't ask for his love, didn't do anything to solicit it except be himself. When Q is upset, though, he's rarely capable of being rational about it. The mermaid was a fool, and he is a bigger fool, since he has no excuse for having decided to do something as idiotic as throw away power and immortality for love. His society didn't encourage him in it; in fact every single one of them advised him against it. It doesn't matter. He hates them too, for putting him in a position where he had to make this choice, for forcing him to decide between Picard and his powers. But most of all he hates himself.
He doesn't know how to deal with this, how to handle the twisting threads of love and hate, passion and resentment, the overwhelming need he has for Picard and his furious jealousy of the work that his lover lives for and his desperate need to pretend he's still independent, still in control of himself. Sometimes he thinks of killing himself. Sometimes he thinks of killing Picard. Effectively in his mind they're the same thing, and he won't do either one. But it hurts so very much.
Unlike the mermaid, he can talk to the one he loves. But he knows his own pain, and the way it makes him lash out, is driving away the one reason he made this sacrifice. If Picard leaves him because he's become impossible to live with, then he will have nothing to live for and no reason at all to have done this to himself. And it will happen. He sees the signs. Picard is withdrawing from him, turning on his captain faade, creating distance. Someday there will be so much distance that Q will be unable to breach it, and then his life will be over. But he doesn't know how to fix it.
Knives cut him to bloody ribbons, but they're not under his feet, they're in his heart.