Apparently, you haven't made it clear to your care coordinator (CC), that too much verbal communicating makes physically, mentally, and emotionally exhausted. This may be caused by how you tried to explain it, but more likely by the CC's inability to comprehend that someone who is capable of talking may not be able to do it all the time.
I don't know what type of AA method you are using, but keep using AA. I do suggest though, that you not use it with relatives, like your father, who are annoyed by it. Perhaps you could spend less time with him, so you won't feel so pressured to communicate. If you go that route, I suggest you compensate for the shorter time spent with him, by also leaving him written notes sometimes.
Yes, you do sound like an introvert. I am one myself. Although I have never thought of myself as non verbal, yes, I could be called partially verbal, as I too don't like to talk most of the time. I find contact with other people very stressful, and prefer to limit the time I spend with people. I live alone, and due to health problems, am no longer able to work, so I am able to limit contact. Because of this, I am better able to handle contact when it is necessary, because I know I will be able to be alone for days, after the contact is over.
I don't know what type of device you have been using, but maybe you should look into others that may be more acceptable to normal people. If you prefer the method you are using now, though, stick with it.
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If a man does not keep pace with his companions, perhaps it is because he hears a different drummer.
Let him step to the music which he hears, however measured, or far away.--Henry David Thoreau