No, there is not a dichotomy between the two.
While there may be portions of each attribute which are at odds, the general notion of 'individuality' may (and does) co-exist with the need for social interaction.
To abuse a metaphor, let us pretend pursing activities which promote individualism is 'chocolate', and pursuing social activities is 'pizza'.
While some people greatly prefer one or the other, generally people like both to some degree. Does desiring pizza preclude a person from also enjoying chocolate as well? Do people sometimes 'overindulge' on chocolate, and so want something more substantial for their next meal?
Does enjoying late night clubbing with friends preclude a person from desiring some solo meditation the next morning? Does spending two years in voluntary isolation mean that one doesn't wish to engage in social activities?