I certainly share your experiences of not having received much in the way of nurturing love from family. My father spent a lot of time away from home drinking and cheating, and my mother experienced the stress of both that situation and the divorce that followed not much later. My grandparents did a better job of parenting, although they still had a hard time with saying "I love you" and were more disciplinarians than nurturers.
I suspect that not receiving this love that we definitely needed has had consequences for both of us.

I know that in my case, I do have difficulty with forming relationships with others. I feel nothing toward anyone in my family except for maybe my grandmother and brother. I have one close friend, and for me that is plenty.

I tend to think that quality is much more important than quantity when it comes to friendships. I also have a number of people in my life who I would consider friends (but not close) and acquaintances.
But actually forming new relationships with others can certainly be challenging for folks in our position.

I know that people can tell there is something different about me, and for many people that is enough to write me off before taking any time to get to know me. But even among people I know well, I still find that I am often not 100 percent comfortable around them, and therefore they still do not see much of my true personality. My closest friend has seen more than anyone else has because he is a rare person I've become completely comfortable around.
I did have one therapist diagnose me as "schizoid," but that was one opinion from someone who only knew me for a short time. She had no knowledge that I am virtually certain I have an autistic spectrum disorder (I didn't know it then either). I'm sure that in my case that disorder complicates matters.
The older I get, the more I am learning that people who are different ought to embrace those differences and even celebrate them. I've spent a lot of time with you, and I certainly don't think there is anything wrong with you.

You are who you are, just as I am who I am. We've both been through a lot in our pasts, and it is difficult for someone who hasn't had issues like ours to understand.
As for love, I definitely would not give up on it. I didn't think I was capable of loving someone romantically until it happened. It took me a long time to accept that was what was going on because of the circumstances. But once I realized that's what was going on, everything started to make sense.
If sexual intimacy isn't your cup of tea, you might be interested to know that I had no sexual interest in this person, even when on T. It's strange because I do have sexual interest in others. But I didn't have any in this person and also not in a few others who I had grown to care about in the past and may have fallen in love with if they had remained in my life longer. It seems that in my case, when I start to really care about someone, I either don't form any sexual interest in them or lose any that I already had.
So I definitely think that it is possible to love someone without having any sexual interest in them, and there are plenty of people out there who have had the experience of loving someone without being sexually interested. You might find there is someone out there who would come to love you but not have much interest in sexuality.
You deserve to have someone special in your life.

Even though I've lost my special person and will most likely never see her again, I feel like it was all worth it. My life is enriched for having known her and loved her. Love is worth it! Don't give up!