I'm the opposite, too intensely caring such that my T was away for 6-8 weeks once and I didn't remember what day/time we normally met so took the entire day off work and just went and sat in the hallway (we were in like an apartment/office building) all day (2-3 hours earlier than the appointment could possibly be) until she showed up! She showed up an hour early but was gracious enough to see me right away instead of making me wait another hour.

Accept that you do care! It's just a little quirk that goes with the territory, don't let it sidetrack you from more important concerns. I showed up early another time when my T had been away and was so early another therapist I knew came through the waiting area and joked with the receptionist, "Well, that answers that question" and I laughed too, correctly understanding they weren't sure when my T was coming back :-) but I was religiously there every time, on time so they could "set their watch" by me

I try to keep clear of my own coils? I refuse to tangle with the parts that are doing things unconsciously; if you were upset, don't bother berating yourself, it wasn't "you" it was your unconscious processes doing their thing and that is just information; you know you really really care about seeing T. If one reacts to the reactions things get all messy; it's like being afraid of being afraid (most of my problem).