Is it me?

This morning I had an appointment with a doctor at work. 9am to be precise. It's always hard for me to get there by 9 but I was determined to do it. I was in charge at work today, a big clinic to run to start with and working with a bank nurse. Rush rush rush, Drop the kids off then navigate through the awful city traffic. A taxi that straddled both lanes and went v slow, bicycles struggling uphill and getting in my way. All the time one eye on the clock. I hit the hospital grounds at 9am exactly. Rushed round parked and ran to the department to see the Doctor. It was 9.05. I booked in and sat down. Another woman was in the room before me. I'd looked in the doctors room and saw he was on his computer. There was no-one in with him.
At 9.20 I walked back. He was still on the computer, I asked the receptionist how long he was going to be.
I had my head bitten off. 'We don't know how long Doctor will be ' She rattled 'He can sometimes be over an hour late. He has a patient in there and you're next'.
How helpful I thought and sat back down. 9.30. The doctor calls the other lady. I began to feel myself get agitated. I was needed at work. Chaos would ensue unless I got there soon.
I returned to the oh so helpful receptionist. I asked why the other lady had gone in before me, as her appointment was 9.30 (she told me).
' Well If you will come in late for your appointment what can you expect' She sharply informed me.
I tried to defend myself that it was only 5 minutes....But she wouldn't listen. I told her I couldn't stay...I was needed at work. She took a marker pen and wrote in big black letters on my records. WOULDN'T WAIT.
I looked at the writing and something snapped. 'It's not that I won't stay I can't' I protested. Her lips pursed and she folded her arms over her boobs.
'Thats so unfair' I cried and then burst into tears. I told them how I was a single mother, how I'd rushed to get there, how, I was running a clinic this morning and how unfair this was.
They all stared at me like I was a freak and I ran out crying.
A failure yet again. Couldn't maintain my composure.
Yet I feel I was in the right, I was only a few minutes late. He was on the computer during my time. He rang me later and admitted he was sending email. But they should have written COULDN'T wait not wouldn't, as that made me seem like some impatient bitch.
I provide excellent care, I'm courteous, efficient and polite. Shouldn't I expect the same quality's for myself as a patient?
Anyways this upset me all morning and at one point I felt so sick I thought I was going to have to go home. But it passed and I'm ok. I wonder if other people would have got upset though. Whether I'm normal? Define normal.