Did I go about this as professionally as possible?

I work a union job. I originally requested a vacation day for today to go to a doctor’s appointment. My manager denied it because she’s too short on Monday’s. So when I came in this morning I informed her I would have to leave early and rather than be pointed for leaving early I told her I would like to use my sick hours. I have them and it’s nothing in the policy that says you can’t use them for early outs. She told me okay. I start at 6:30am. My appointment is at 1:00pm. I’m on public transportation so I finished my task by 11:00am and came down to my manager and informed her of that. She goes “Oh. You cannot leave this early. I have no one to cover your floor.” So it went from her approving my early out to “I’m leaving too early. There’s no one to cover your assigned floor.” Mind you she never mentioned how early I could leave, she never asked how early I was leaving and she knew when I told her earlier that my floor would need to be covered. Rather than argue with her. I asked her to call our union rep down. My union rep come down and tells her that she can in fact use my sick hours and not point me for leaving early. My manager still fought it. So both I and my union rep just agreed that we will file a grievance toward the point. We didn’t fight her but tells she took it personal because when a grievance was mentioned she said “You can do that. That’s fine. I’ve been grieved before. Doesn’t bother me.” And it screamed that she was in fact bothered by the fact I didn’t budge. I didn’t argue. I still left early. Took the point and informed her it will be getting grieved. I believe her mood from earlier changed. She’s stressed out about her duties as a manager and when the time came for me to leave early she took that out on me. She thought saying she was gonna point me and not use my sick hours and gaslight me with the “I have no one to cover your floor.” It would make me stay and that way she won. It didn’t turn out that way.

Did I go about this as professionally as possible?
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