It's easy enough to reduce Criston Cole's Episode 5 behaviour to being in love with Rhaenyra, but the truth of the matter is that his reaction doesn't revolve around her so much as it revolves around his struggle with honor and purpose.
As he said back in episode 3, Kingsguard is the highest honor that his house has ever had. What he and Rhaenyra initially had was very much reminiscent of the courtly love that was dominant in Arthurian legend, the concept that a knight and lady could have affections for one another while respecting the boundaries of their stations and maintaining a sense of "purity".
It's already been discussed that the episode 4 conflict of to-sleep-with-rhaenyra-or-not-to was not 100% consensual because Criston was in a position of subservience to Rhaenyra and it was very much a "damned if you do, damned if you dont" situation. He risks death either way and ends up breaking his vows to appease her. Of course, it is apparent enough that he harbored feelings for her. But two things can be true at the same time.
We open to episode 5, where Criston proposes that they run away and marry one another, already without his armour and showing his vulnerability to her. When Rhaenyra rejects, he tells her that he broke his vows as Kingsguard and thought that marrying her would relieve him of his guilt. Guilt over what? Breaking his vows, of course. When she suggests that they continue on as lovers while she married Laenor, he reduces it to being her "whore".
In Criston's eyes, the only way he can properly make up for his sin of breaking his Kingsguard vows is by swearing the vows between two people in matrimony, another lifelong commitment. If it was simply about love in his eyes, he might have said "lover/paramour" but he specifically says "whore", someone who trades their body for coin.
Having his proposal be rejected by Rhaenyra was not simply the loss of a romantic future he thought they could have, it was the loss of his chance to redeem himself and regain the honor he lost by sleeping with the woman who gave him his job and whom he was sworn to protect.
It's why he loses all control over himself when Joffrey tries to build a rapport with him and insinuates that they are on the same boat. Criston does not want to be Joffrey's equivalent, a "whore" for their King/Queen to enjoy. To him, there is no honor in that. But the reality of it is staring him so plainly in the face during the feast that he needs to eliminate that reminder by attacking and killing poor Joffrey.
That inability to live with the reality of his situation is further emphasized when he finally tries to kill himself. He's more than a scorned man, he's a man who's lost his purpose and blames himself for it (as seen when he admits to Alicent that he slept with Rhaenyra and accepts the fate of death).
When Alicent stops him from doing the deed, what she is essentially doing is giving him a chance to regain his honour and a new sense of purpose: serving her and her children. It is possible that they will have the courtly love that is more true to Arthurian legend, Criston having such a deep devotion to his Queen and his role as her guard that he pushes the chess pieces to further the Greens' cause. Whether or not there will be a semblance of romance between them in the time jump, there will no doubt be the devotion that renders him one of Alicent's staunchest allies.