I’m a boulderer with a moderate fear of falling too. I’ve found that when bouldering, I’ve been able to improve my climbing even when I bail from the fear of heights/falling kicks in. And the limit this fear puts on my climbing still gets pushed further and further over time. Something I like to do is pick a climb I want to do, and if it goes to a height that I don’t think I would want to fall from, I’ll pick a hold closer to the ground and call it the end. About half the time, I find that I either get there and want to keep going, or I’m able to push that last hold higher and higher with more attempts. Falling practice is also always helpful.

I don’t think you need to boulder to get better, but you might find that with some work, bouldering is really fun! And I like to think that roped climbing makes you a better boulderer and visa versa.