You and Barb are not playing the same game.
These problem manifests while you're playing the game. But these in game issues are just symptoms of an out-of-game problem:
You and Barb are not playing the same game.
You and the barbarian player have a fundamental disagreement about what game you are actually playing. The game you are playing is:
I sign up to play D&D as a co-operative party, not babysit/worry about PCs constantly attacking other PCs.
The game Barb is playing is:
constantly attacking other PCs
These are two entirely different games, even if they are both called "D&D". And since you are both playing totally different games, there is no way to resolve this conflict in-game. You both have different rules and expectations when approaching the game, so this cannot be solved through in-game role playing.
It's time for a reset: the whole table needs to have a conversation about expectations, specifically, about player versus player conflict.
You're not having fun. You wanted to play one game, but instead, you're playing a different one that you never wanted to play. So you need to talk about that. You need to communicate with the other people at the table about how the player versus player conflict is not fun, about how you had a totally different set of expectations when approaching the table. But you also need to be prepared to listen: let the other players communicate to you how they feel about the conflict. It is important that everyone understands where everyone else is. Understanding one another is the first step.
Once you have an idea of where everyone is with this, then you have a conversation about working toward a favorable outcome for everyone. Again, I want to emphasize, we want to be working toward maximizing the fun for everyone. What this does not mean is something like this:
I'm not enjoying the PVP. I demand that it stops.
Something like this may satisfy only you at the expense of everyone else's fun. We don't want that, so a better first approach is to work toward favorable compromise:
I'm not enjoying the PVP conflicts. Can we brainstorm some ways to change how we handle them, so that I can have more fun, and we can still preserve this character trait in Barb?
Maybe this looks like putting some limits on when and how Barb's bloodlust triggers, maybe this looks like making it easier to end Barb's rage, or maybe this looks something like "how about Barb just doesn't attack me". This is for you and your table mates to work out together as a group.
Know when it's time to give it up.
D&D is fun. When done right, it can be the time of your life. But playing D&D when it isn't fun? It's worse than going to work and not getting paid for it. If your fellow players are willing to compromise with you, and you are able to playtest some solutions and find something that works for you, that's great; this is the best outcome you could ask for. But if they don't want to compromise, sometimes you just gotta cut bait. It is often said "No D&D is better than bad D&D." You just have to be prepared to look for another group if the current group doesn't want to change their game.
