Yes, it seems your T messed up by not giving you the chance to inform p-doc.

I would discuss it with T (as well as your concerns re her ratting you out) and give her another chance. But T's actions showed she did not trust you, so I think it really needs to be addressed if *you* were to be able to trust her i.e. what T did would not inspire trust in me, as a client, either. Trust is a two-way street. T messed up here