It would hurt to hear my therapist is strained when my appointment comes around. That would be very difficult and hard not to blame yourself for.

From a outside perspective this is what I'm hearing. She tried to accommodate some patients with tight schedules, gave it a shot and it just didn't pan out. The work day gets to her by then. Since she's giving you other appointment times I wouldn't consider it unprofessional because even though it's not fun to figure out she's a person who has to make sure her own well-being is doing well too.

Otherwise, she shouldn't be able to fully pay attention to you which wouldn't be fair. It's your hour and she should be fully alert and ready to listen and comprehend everything you're bringing to the table. I would think that continuing doing a time where she can't be on the ball would be more unprofessional than switching times.