That’s not technically a phobia, I think. For it to be a phobia it has to be extreme (it doesn’t sound like it is) or irrational. There’s nothing irrational about disliking a situation where there is a very real risk of serious injury or death. It would be like saying you were phobic about travelling in cars driven by drunks or about arguing with muggers.
I used to get the sweats/shakes with heights in situations where the risk of injury/death was negligible e.g. close to windows at the tops of skyscrapers. It seems to have gone away to a large extent though. When I was young I climbed up here a lot (the view starts at 4:10 or so). The balcony’s narrow and the guard rail not so high.
Rincewind the wizard in the Pratchett books always sat in the middle of the flying carpet hanging on tight.
Someone said to him, “Are you afraid of heights” “Oh no” he said “I am not scared of heights but I am scared of drops”