The two books Ive read on the history of College football indicate it baegan at the College level, not high schools. With it begining in the Ivy League, and Harvard in particular in the 1870's. All the starters on the Varsity team would receive their jerseys with the big H on it to keep, while everyone else did not.

This got expensive so eventually it turned into a letter sown onto a sweater (it is cold up there after all) and eventually a leather jacket.

FWIW this also appears to be inline with the Wiki article.

The Books:

Rites of Autumn: The Story o College ootball

and

The Opening Kickoff: The Tumultuous Birth of a Football Nation