I have no children. I live alone. I've been socially avoidant all my life. I have a significant other, a boyfriend. He is 18 years older than me, and his health is poor. I see myself being alone for most of what's left of my life. I am sad about feeling like I don't belong to a family, which I think is how humans are designed by nature to live. So I think I experience sadness that might be somewhat like the grief you express.
In my case, the grief is less specific to not having a child, than to the aloneness in general. I moved far away from my family of origin, and distance does erode closeness. My sisters have their spouses and children, and I doubt if the thought of me even pops into their heads over the course of a typical week.
I think having a child can have a special appeal for someone who is socially avoidant. I can't imagine lacking confidence around a child of my own, as I do around people in general. I feel I am a loving person and would have been a good mother. I can't imagine losing my child's love, in the way that I feel I have lost the affection I once found in relationships with siblings, neices and nephews.
My grief is not for the exact same reasons as yours, but it is real grief and I am very depressed, a lot of the time, over this aloneness. I don't think human beings are meant to be alone; it's in our DNA to be intimately involved with others. The pain does leave me at times. So I ask myself how does that happen, and what can I learn from it. Being involved in something that interests me has helped. So I tell myself to try and find more opportunities to do that. I think that's the best advice I can offer.
You are a nice and warm person. I'll bet there are people who would like to know you and spend time with you. Overcoming the reluctance that comes with avoidance might open up something to increase your satisfaction in life. However, I tell myself the same thing. I don't seem to take my own advice, so I guess the most honest thing I can say is that it is very painful to have the trait of avoidance.
(((HUGS)))