I've been under once, in a medical emergency.
The hospital did everything they could possibly do to ensure that I was ok - even when I was having a panic attack. Just like everything else, communication is the key - make sure you have a list of your allergies.
Talk about your level of fear, the doctors, and the anaesthetist will be able to make sure that you're ok, don't be stoic and try to just get through, take what's offered, and let them know if it's not effective.
They will do everything they can to care for you, in a way that makes you feel cared for and comfortable.
You can do this.
Rowan