You offered solid advice, but you also F’d up.

The FU was in the “So I told her some nasty things I’d heard about her boyfriend and doubled down on the recommendation to seek therapy” bit. You’ve now cheapened the therapy rec by tying it to some petty gossip. (It might not be petty gossip, and sounds like it wasn’t, but if she’s not ready to hear it then that’s how her filter/rose-colored glasses will perceive it)

It’s a very minor FU, and I don’t think it changes anything, ultimately. But it does mask the very true and enduring need for therapeutic help with your momentary frustration and ire.