The title of your post caught my eye because I too have struggled a bit with loneliness and shyness in sobriety.
I'd already isolated myself almost completely by the time I sobered up. The few people I was still in contact with were relationships that revolved around drinking or smoking weed and I cut those people out of my life.
So, I found myself with no friends at all. When I was drinking I wouldn't have cared because I would have been happy drinking alone. But I was particularly worried about that during the first few months of recovery. I wanted new sober friends. I started taking yoga with thoughts toward making friends, but I would be so anxious that I wouldn't open my mouth the whole time I was there and would leave as soon as class was over.
Now, I'm going on 7 months sober. I still don't have any close friends, but I feel much less worried about that than I did early on. I've settled into more things that I like doing and feel more comfortable on my own. And the social anxiety has mostly faded. It's becoming easier to talk to people at yoga. I am slowly starting to get to know everybody and they are starting to get to know me.
When I get impatient, I remind myself that it took me years to make my pot-smoking, drinking friends. It's only reasonable to expect that it's going to take some time to find sober friends. Relationships aren't built in a day, they are built up over months or years.
At this point, I'm happy to focus on being who I want to be and getting my life in order so that I'll be the sort of person that somebody might actually want to be friends with. And maybe more importantly so that I'll be the sort of person that I want to be friends with.
So, my advice would be to just keep going to the meetings and the martial arts classes. Whether you talk or not, you're making progress in the right direction. With time, you'll feel more comfortable with the people and start to get to know them better.