Anxiety in 9 year old, how do I deal with this?

My daughter is extremely anxious, like intensely, when it comes to doctor or dentist appointments and today we went to the community pool and they wanted her to do a simple swim test to make sure she was able to swim without a life jacket and she freaked out, started crying, crossing her arms, acting like it was the end of the world, and in the end we had to leave because she wouldn't do it. I can't begin to explain how intense she acts, but only in certain instances, most of the time she seems fine, shes not shy, she's confident in herself .

At doctor's and dentists she is defiant and scared of every little thing they want to check. I've never seen anything like it. At the dentist last time, the second they took out the cleaning tools she got so scared and startledly threw herself onto the floor, curled up in a ball and started crying. It turns out she needs some work done which requires anesthesia, and she was prescribed a pretty heavy anti anxiety med to take before the appointment, but I'm still scared she's going to give the dentists a hard time even with that, she already goes to a specialist who works with difficult and anxious kids.

On another note does anyone know if they use gas or iv for kids anesthesia at the dentist?

Anyways I'm just lost and I feel like a bad mom not knowing how to handle it, I hate to say it but its embarrassing when she acts like that. I do my best to talk her through it but in the moment nothing ever seems to work. I feel like she's too young, and doesn't have anxiety everyday so I don't know if medicating her is the best way to go and I just know if we go to a therapist she's going to be defiant and not want to talk to them.

Any advice is appreciated ❤️❤️