I always play the same tees at the same course. Is my Handicap Index® "established" from that set?

A Handicap Index^® is not established from a particular set of tees. Every time a score is posted, it is converted into a Score Differential™ that evaluates your performance as if it were made on a course of standard difficulty.

As a result, your Handicap Index^® is a portable number and each time you play, it is converted into a Course Handicap™ as if you are playing that course for the very first time. (Rule 5, Rules of Handicapping)