Welcome to the forums.
In the realm of relationships, 4 months is a relatively short time, and from what you say, it sounds like your girlfriend has no idea what she wants, and it is she, not you, who is insecure.
I do agree with her in that each of you needs your own lives, BUT, to me, saying that you spend too much time together and asking for more space does not bode well. It implies that she's tiring of you, and if that's the case after 4 months, then what after 6 months? a year?
