Hey, recently I had to have fillings for the first time and I was terrified beyond belief, I actually held my breath so long I got dizzy because I was so scared but you will not be sick. When they inject you it might go a lil in the back of your throat. This won't make you gag but it doesn't taste altogether pleasant. Just warnign you because no one told me that and I freaked when i tasted it LOL but it was fine. Then they leave you 10 mins while it takes effect and then they get to work. Tell your dentist you are nervous and you wanna know step by step what he is doing. That helps. Altogther I'd say it only takes 20 mins.
The swallowing thing gets me so make sure he knows if you raise your hand he is to stop. My dentist was fabulous about that, If I so much as twitched my hand he and the asisstant pulled back straight away til I was ok. That control was fab. But overall it seems worse right now than it will be. It will be over so fast you'll be suprised i think hehe.
Good luck babe and remember you won't V* and you are in control 
xxxxxxx
Be courageous, believe in yourself, and be the best woman you can be. I'm with you all the way.