This might be an example of the tail wagging the dog. You claim to have difficulty with speech production? I don’t know you, but that could be the case. Perhaps there is something organic underlying this issue. But it’s also rather obvious that you are self-conscious about it as well, so you are focusing a lot of your attention on your own voice, resulting in it perhaps sounding more “off” in your mind than it really is. The label “social anxiety,” like most psychological abstractions, is so vague as to be practically meaningless. Yeah, you might be anxious around others; most people with any form of perceived physical or functional impairment are to some extent. But it sounds to me like what you are dealing with is not “social anxiety,” but “vocal anxiety” (trademark pending). There are probably two potential solutions to that issue:
1) Seek out a speech therapist in order to attempt to establish a “voice” that brings you confidence, or
2) Simply accept your voice for what it is so as to pay less attention to it, and be less bothered by it, which might help you be more comfortable in social settings.