I'm playing a character in a DnD setting who decided to become an adventurer because it sounded like fun, not seriously considering how dangerous it would be. Our DM has us running a campaign with a wonderfully antagonistic storyline where our party has unwittingly tangled itself in a battle with elder gods that are vastly more powerful than the party is. The result of this for my character is that he is deeply in over his head and is absolutely, constantly terrified. Eventually, I want to roleplay my character overcoming his fears and becoming confident in the face of danger, but he's currently at the point of coming to terms with what he's gotten himself into.
I'm not sure how to roleplay this effectively. If interacting with the other players wasn't a concern, I would have probably had him run away from the adventure by the point the campaign is currently at, but that would be an egregious case of my-guy syndrome. Sticking with the party, I've frequently had my character become paralyzed with fear or overreact to other characters' decisions that he believes put him in more danger. I'm nervous that this could quickly become annoying for the people I'm playing with. In other situations, my character simply handles combat well, but I don't think this is an accurate reflection of his emotional state.
How can I roleplay a character who is feeling deeply afraid of what's going on around them without disrupting the game for the other players in my group?