First, your feelings are very real and there for a reason.
It feels like this is triggering you on an inner level.
It is almost as though you have two minds with this - the adult mind who wanted your friend to have access to the same quality of mental healthcare you have - and then a younger part who feels the twinges of jelousy.

I may be way off base here but wanted to share incase it can help you. But it feels like there may be something in the past that is the root of this. It is almost like there may have been a time in your life when you NEEDED an adult (parent or close teacher) but someone else - a sibling or friend - would interupt you expressing your needs. The authority figure would shift gears and focus attention on the other child. That would leave you out in the cold.

It feels like you wanted to make sure the other child was "ok" too... so you didn't protest this. But deep inside, you held resentment because your needs were not being met. That made you feel badly because you were trying to not be resentful of the other child getting what they needed.

??? Anyway, that is what I see. It looks like you have a big heart.
Just remember that you do have a right to have your needs met.
You have a right to be heard.
I would bet that your T may have intentionally put the apts together because T thought you would like to touch base and see your friend there. Some people like that. But sometimes it doesn't work.

It reminds me of my dentist. My ex - who was a primary abuser of me - goes to the same dentist I do - since we saw the same dentist while together. Well, my new S/O started going to the dentist. She would go when I didn't need to go. Often, she would be upset when I asked her how it went because she kept running into my ex. Soo.... after two years of that, she finally told the receptionist "Do NOT put me down on the same day as XYZ!"

The receptionist was in shock! She said "Well I know you guys know eachother and I thought you were friends! So I have been putting you down on the same day figuring you may want to go get lunch together!"

Bottom line is that people do tend to try to do what they think is what we would like. But they can be wrong. It is our job to let them know what we need.