Reaching out can be a scary step. I'm glad you are trying though.
As Halloweensky suggested, maybe wiring things down (either list or paragraph) would be helpful. I regularly do this, both with doctors I've known for years, and new ones.
Another option might be to tell them over the phone if you are more comfortable doing that. It can be as simple as telling them you want to see the doctor for mood concerns (or whatever name you want to give it).
Most doctors, at least here in the us, will ask about mental health stuff in their initial history questions. I've found that simply not being able to answer those questions gets the doctor to look up from their screen long enough for me to nod...
I hear you saying you are worried about the doctor following up on your last visit. It might be a good way to lead into a conversation about your mood. If she asks about the referral, you can tell her that you chickened out because your parents were there, but you'd like to revisit the idea now. I'm guessing she has seen more than one patient who was nervous about following through on mh referrals due to family presence... also, that was 2 years ago. A lot can change in 2 years... I'm guessing she won't be mad or frustrated that you "didn't listen" the first time around.

Good luck. I hope you can make the appointment and manage to talk to her. I also hope she's receptive, which it sounds like she might be since she offered up a referral before.