I know just what you mean and sympathise. I certainly don't think you are alone in being alone.
When I was young my parents moved around constantly and I attended 14 schools in 13 years, none for more than two years' running. I coped quite well with this until I was 11 and my mother left my father and the emotional strain added to the moving caused something of a social and emotional breakdown in me and I found it more difficult to connect with others. I was a great reader, though, and turned to books for company and solace, something that was easy to do as I am introverted by nature. The more we moved the harder I found it to make friends,especially as, by then, everyone else had found their own circles and networks.
However, I made an effort when I went to train to be a teacher and made friends at college and at each of the schools I taught at. My big 'break through' was to meet my DH quite young and we became each others' besties. I have since shared his childhood friends and we have made friends as a couple.
Since I retired though I have led a very solitary life as I have lost touch, except by e-mail, with my work friends and my DH is out 12 hours a day working.
I know I could make some new acquaintances by volunteering or getting a job but I have somewhat lost my confidence and I think I am a bit of a prickly person. I certainly fear rejection and would rather not court it. And, of course, the older you get the harder it is to make new friendships with others who have lifelong relationships.
I often wonder what it would be like to have school, university and work friends like my own children do. They never had to move and could put years of 'spadework' into their relationships.
One thing I have learned since retiring, however, is that loneliness and being solitary are two separate things. Loneliness is awful but solitude, if not forced upon one and if for contained periods, is a luxury. It is wonderful to be 'far from the madding crowd' at times.