Yes and No
Yes, I sometimes get a funny feeling while on my own. It has served me well. At times, while travelling, it has prompted me to move seats, hostel, country and I find out later, usually on the news or in the paper, something bad happened at the time I should have been there, like a bombing, landslide, tourist food poisoning, room robbery, etc. Sometimes I look around and see some creepy person or a spider staring at me.
No, I loved going out on my own when younger - movies, cafes, theme parks, restaurants, bushwalking, snorkelling... Now I'm engaged I settle for the solitary coffee at the cafe while he's at work.