As the name suggests, I'm looking for an odd sort of story where the main character/hero professed his love to a girl and got shot down, but now in one way or another is stuck together with her. This "stuck together" can be anything on a broad range. They could be stuck living together, or privy to a horrible secret that forces them to work together, or they could be forced into a partnership of some sort, or you could even have something like Maga-Tsuki or B-Shock where the hero and heroine are literally unable to leave one another's side (or at least unable to get more than a set distance apart).
Frankly, I've seen a ton of series where the hero has some big rejection in his past that hurt him and had a big effect on his life, but in just about every one I know the girl disappeared before the start of the story, never to appear and interact with the hero outside of flashbacks. Are there not any reversals then, where the girl who crushed the guy is forced to remain at his side?

You could try Masamune-kun no Revenge. The main character seeks out revenge on the girl who rejected and humiliated him.

Jitsu wa Watashi wa . The main character confesses to a girl who rejects him but then later on starts to fall for him.

Not sure about those two. In Masamune-kun, the girl isn't STUCK with anyone, she's not in any situation where she has to be around him. Masamune's just chasing her down. Not to mention that she has absolutely no clue about his identity or situation and thus is unable to share one bit in the awkward situation. And in Jitsu wa Watashi wa again there isn't that much requirement: she just chooses to stick with him. Not to mention that he'd already moved on.

The closest I've seen is Pastel. In this series, Mugi falls for Yuu almost at first sight, but he says some dumb things that get him a slap on the face, and then she leaves before he can say anything to apologize. Then he goes home and finds her in his bath because their parents were friends and his father promised to take care of her if anything happened to her father. Now the two of them are stuck together living in the same house. It's not a perfect match, since he hadn't made any confession and actually takes care to make sure she doesn't know he's in love with her for many, many volumes. However, the way they're suddenly forced together right after they have a falling-out is a great match.

What I'm looking for is a situation where the feelings haven't changed: the boy is still hurt from the rejection but still has lingering feelings, and an outside force makes it so that the two have no choice but to stay together or at least to be together regularly due to some sort of arrangement. For any amount of resentment, hate or vengefulness has not taken the place of the person's love, and the love hasn't moved to another target.

Itazura na Kiss comes to mind. Though it is the girl that gets rejected. And the author died before finishing it but you can watch the anime for the planned ending...

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~4400 manga completed
~1700 ongoing...

Forgot about that series. It certainly is a gender-reversed version of what I'm looking for.

One thing I'd like to make clear: it doesn't have to be a harsh rejection. Something like a friend who tries to let the guy down easy, maybe because she likes/is dating someone else or just because he's "just a friend", is completely fine. A rejection doesn't have to be insulting or sadistic to hit like a sledgehammer and hurt for a long time after, and since part of what I'm looking for is that awkward situation, the added awkwardness of having rejected a dear friend is a bit of a bonus.

These mangas don't have the "dumping part" but the protagonists are "stuck together".
If you want to check them out:-

I Hate Love (by Lee Kyuh Wool)
Shikigami Danshi
Tian Jiang Xian Shu Nan
The Jinx's Lover

Cherry Boy, That Girl (where the guy sticks to the girl on his own even after getting dumped).