AITA for it not being my problem?

I (54F and on the larger side regarding weight) was running late for a respiratory appointment. I can barely walk across the room due to just recovering from pneumonia twice and two and a half months of covid. And so, my child (19F , 5’0 and my carer) was there to push me in a wheelchair up to my appointment. While trying to find a parking space in the disabled area (I have a badge) I saw that two cars were about to pull out and so I waited. Once the first car had gone, just as I was about to drive into the space, a women with oxygen prongs and an oxygen cylinder in a backpack (I’m guessing in her 60s) walked into the space, waving her hand towards her husband who was in their car and put her hand up to me, telling me it was hers. I’m British and I was taught that first come, first serve and that holding a parking space by standing in it does not give you priority to that space. And so I told her to move and started driving forward. She began shouting at me that it was HER space. I slowly kept driving towards her until she moved. At which case, she stayed beside the car on my daughter’s side fuming near the window, staring at her. Once I’d parked, she circled around and knocked on my window shouting how she “HAS BEEN WAITING FOR A SPACE FOR OVER AN HOUR”. At which I replied “THATS NOT MY PROBLEM”. At this point the other car that was about to leave had already left and her husband parked in there while she was shouting at me, repeating how long she had waited. I guess, I have felt like an asshole ever since because she had oxygen but the protective mum in me was thinking of my daughter. She has to get the wheelchair out of the car and push me and I don’t want her pushing me any further than she has to. While the woman had an oxygen mask, she could clearly stomp around my car multiple times, while screaming, while I did my best to keep a straight face. Even seeing my disabled badge did not deter her from her rant. She eventually left when her husband locked the car and started walking away.