Social interaction between PCs can be an interesting beast. Everyone at the table is - generally - there for the story that their PC is going through. Yes, they're also their for the group and the social interactions, but a player's job is to portray their character in that story so it makes sense that ego-centric focus (to use an unkind term for it) is on their mind.
This, combined with most people's natural tendency to try to avoid conflict, and it's not surprising that even if two PCs don't get a long, or have a problem, that seldom something comes out of it. But what about if someone wants something to happen?
Well, the trick here is that nothing is going to happen unless both players want to get involved with it. Without that buy in from both parties, you just end up with the drama equivalent of unrequited love where one person hints and flat out states there is a problem, and the other person doesn't respond because of any number of reasons, including just not being aware of it or being unsure what to do. Alternatively, the person going for drama just becomes a dick causing problems and derailing the rest of the game again and again.
This is why out of character communication is very important. Believe it or not, In Character drama is best done with out of character cooperation between the two players. Together you can work out what happens, when, and where things will go. Yes, it may feel a little less spontaneous when it happens, but that ultimately shouldn't matter for two reasons.
First, in working out things with the other player you are effectively RPing out the interaction and deciding how it is going to go, so it's not like your forcing the character into a thing. You're just figuring out how it plays out before the other people at the table do.
Second, no one else at the table is privy to that discussion and so it will still feel real and great for them.
Think of it like putting on a show. Afterall, in an RPG the other players are the audience. So give them a show. Make it fun. And maybe learn more about your character in the process!