Yikes, I've experienced a few issues like this, when people try to dictate how you go about conducting your therapy/HRT/other issues, like they understand a process they've never experienced. I know it's not super similar, but back when I was getting my top surgery letter from a therapist, my parents kept suggesting what I talk about with him (we were fighting quite a bit, between the three of us) and insisted I had anger issues without understanding that they were my biggest triggers in suggesting how I conduct therapy. So yeah, pushy, nosy, "mother knows best" attitudes are the worst, and it sucks you have to push through 'em, too. If it were me, I'd just tell that friend that how you go about treatment is between yourself and healthcare professionals, and you'd like to keep it that way, since she clearly has nothing nice to say about your journey toward transition.
On a happier note, here's to hoping you get your letter and T sooner than expected! That's always a happy moment!