Can two insecure people work in a relationship?

Anonymous
My boyfriend and I have only been together officially a month and we're both pretty insecure and anxious people. We both worry about everything and care a lot what people think of us and I think this comes out in the relationship. We kind of have to keep reassuring one another we're into them still, him more so than me, as he keeps saying I'm out of his league. He tells me I make him happy anyway that i've chosen him.
I'm a blunt person, with a blunt sense of humor and sometimes some of the things I worry have offended him due to his past but he jokes about it, mainly as a coping mechanism I think. I can laugh at myself, but I worry too much if I've hurt his feelings, even when he tells me I haven't. I tend to apologize a lot without realizing, and he jokingly tells me stop. He struggled to grasp at first that I was fine with his interests in nerdy crap, where in the past he was judged. Anyway, I'm worried that even though things are okay now, could this potentially be a destructive relationship? He told me that in arguments he needs to get out for the house, instead of communicating the problem. I can't work like that. I'm a very caring person so I support him and his struggles and he does with mine.
Does this sound like it can work?
Can two insecure people work in a relationship?
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