While I cannot answer your question specifically (though I do suggest you get in touch with your Plot team as others have said), I would like to offer you a couple of a mental exercises all centered around the question of "what does it mean to your character to be immortal?"
1. How does your character view shorter-lived races?
I fell down into this rabbit hole as my character and it ended up being ridiculously cool. It's a big question. In my character's backstory he is closest to other MWEs, Dryads and Kyn. Kyn live very short lives (~30ish years at the high end) so I had to think about how he really thought about that. For instance, I have told people in-game that Durnic wasn't even sure what he was going to do until he was 30. This completely blew away an orc that he was talking to at one of the last events I went to.
This is an interesting question, too, because you have multiple ways of approaching it. The first is that you could approach it with a caretaker mentality where you like to put yourselves into their shoes and live vicariously through them. While as a MWE you might consider marriage and child rearing to be a decision that might take you a century to come to grips with and want to do, you could have been the god parent to six generations of Orcs or Kyn. You get to see them grow up, learn, fail and die while remaining somewhat distant to the entire thing.
The second is that you just don't let them get close to you at all and instead you view them as pets or tools. Sure, they are stalwart companions, loyal and sometimes sweet but you know that their life on this world is limited and they will eventually pass. You will mourn their passing as you would a dog that you raised since puppyhood but you still have that emotional isolation from them. You will never get used to them passing on, of course, but you still know deep down that it will happen.
2. How does your character perceive time?
Durnic is a military man and trying to play that balance between understanding that a hill has to be taken right now but still knowing that sometimes a hasty decision will affect the world for a loooooong time has been a fun conundrum. There are some things that a MWE can just wait out instead of really worrying about it, like a long prison sentence or a slightly obnoxious ruling family. As long as they aren't tyrants, you are not likely to get involved. Or, at least, you don't have to.
3. Does having a long life give your character any quirks?
I have been RPing Durnic as kind of the "last of the old blood" mentality. I swear in horribly-butchered Sindarin, which no one else from my Vale does, and reminisce on how things used to be. He will chastise the younger MWEs from his Vale for not sticking to tradition in a grandfatherly way.
As a military man, Durnic has also Seen Some Stuff(tm) and I play him as having a thousand yard stare, PTSD symptoms and, unlike every other MWE from his Vale, he is not cheerful nor super outgoing. He has his moments where a character can break that mask but they are few and far between. (As an aside, I am doing this partly as a way to understand how PTSD has affected my father, who is a Vietnam veteran. We have spent many nights kicking back and discussing his issues after coming home.)
4. Does your character have long-term goals?
When I say "long term" I mean goals in the coming centuries that aren't actually likely to come-to-pass in this LARP but something that you should mentally be thinking about anyway since your character likely would be too. Your character can live long enough to see civilizations rise and fall, continents shift, and the very fabric of magic change. You should probably be thinking beyond just the current Plot line you are involved in.
All of this, of course, can be RP'd any way you like. You could be a very young MWE and play it out as that nothing like this has ever really crossed your mind or set in yet. You could play a very old very MWE instead where you have thought about these things in-depth and fleshed it all out.
A note about metagaming: Being outgoing and involved is much more likely to net you a good time at a LARP instead of being a sit-in-the-back-and-be-surly. The latter playstyle has been fun for me, but I have been told I am doing a good job of riding the line. I should also note that Durnic is my second Alliance character, not my first, so I am aware of the general game atmosphere and what I can and cannot get away with.
Edit: I apologize if any of this is disjointed, I typed it up over the course of a couple of hours between meetings and other work obligations.