""Use BMI unless you are an athlete it is the best way.""
It isn't. Taking your clothes off and studying body fat, muscle mass and lifestyle, is the best way.
""At 5'3, my ideal weight would be around 8 stone. Most people would say "that's tiny" but that's actually healthy. ""
That's healthy for you. I've been medically underweight and at 5'2", I wasn't that light. My choice of exercise is a lot of walking and free weights, so my muscle mass is excellent.
""Dangerously overweight means being obese.""
It can mean dangerously overweight for your medical condition and I think that is what she meant.
OP, you need to explore this further, with her, not on here. I think you need to look into the best exercise, on account of your arthritis and get a proper plan.
You are nowhere near being dangerously overweight, in general terms.
I've been seriously ill and depressed. I'm really annoyed that my Consultants kept fobbing off my weight and wasn't more blunt. I started summer with six stone to lose, I've lost nearly three, but they should have been more honest with me. Perhaps that is what she was doing.