Most people feel this way. To your friends and everyone else who has seen you in your 'confidence mode', you don't feel pressured to prove anything. They've already seen what you're like when you're at ease. Strangers and new people don't know anything about you so you feel the need to prove yourself which has the adverse effect of making you insecure and awkward. It's perfectly normal. 

It also means that you're not confident in yourself at all. True confidence comes from within, not from outside validation.