I do not like talking to random people in public. It causes me anxiety.
Well it could be a case of social anxiety! nervousness un social situations! no big deal
I am comfortable out in public but do not like random conversation with unknown people.
I get you! it has happend to me actually near 90% of the people report feeling a form of social anxiety at some point in life
I can see that number being accurate. It is not uncommon to experience social anxiety at some point in your life.
I will like to star studying well being, is a much studied topic in psychology especially positive psychology to help people overcome this problems!
I would consider help and treatment if my anxiety became worse. 
You have to be carefull not to let it sclate to panic disorder! recurrent unexpected panic attacks, start now and you will overcome it