I feel like most people are like this. It's practically human nature to be afraid of other people judging you (why do you think the fear of public speaking is so common?) and everyone feels more comfortable when they have friends around. I'd hardly call it a "dependent personality problem" - that almost sounds like some kind of disorder. Really it's just a problem with how the average human is wired - nothing to stress about.

So just remember if you meet a stranger and you're sort of awkward standing next to them, bear in mind that they just might be feeling the exact same way. You're not alone in this.