INTJ or something else?

[Compost]

I've always tested as an INTJ and the description fits me pretty well for my school activities. Being right, having the only opinion worth anything, taking charge when everyone else is incapable, the way projects are carried out, etc. But I also have an emotional side of despair and inadequacy. This is not from intellectual inadequacy, but social. The only thing that keeps me going through the say is knowing I'm more capable at school than anyone I know. Being introverted really gets to me and I become envious of anyone who is in a relationship or has an extravagant social life. When I'm depressed I always try to analyze what's wrong and how to fix it. Even though this is the case, I never feel capable of executing the solution. Is this envy, fear of being inadequate, and sensitivity part of being an INTJ, or is it a different type?