Yes Children can have anxiety and fear of people just like adults.
When I was 3 I started developing anxiety and could not be around people without being scared and anxious and I'd always go hide whenever family came over to our house or strangers.
Even when I started Kindergarten I was always shy and avoided people and had anxiety around those people and although now at 30 years old almost 31 I still have some form of anxiety so although the anxiety has gotten a bit better it's still not fully gone.
Sometimes talk therapy may help with social anxiety while other times it doesn't do any good like for me.
I had talk therapy when i was a kid and it never helped me and actually seemed to make my anxiety worse.