I used to be terrified of the dentist when I was young, probably because the woman I had was referred to as 'the butcher' by my classmates. And she was. One time the numbing injection didn't work (cue 10 miuntes of torture xD). But I think looking back, it was deliberate on her part, she was a horrible woman. Anyway, that is worst case scenario and highly unlikely, plus you are an adult so if you scream they'll take you serious and stop xD
The turning point was when I was older (and had another dentist) and had to get 6 fillings renewed! And she did one side and I thought, 'feck it' and just asked her to do the other side too. I had resigned myself to it. And you know what, it finally clicked - the fear before hand is the worst part.
Now at 30 I have a lovely dentist. I always ask that if I get an injection, it has to go up and into the gum, little by little. That way it doesn't hurt much. And then I focus on trying to stay calm and still.
I still get nervous going but I think telling yourself that provided you have a sane dentist, the nerviousness before is the worst part. I mean, a filling takes no time at all and with the injection going up into the gum, it isn't a big deal.
I once chanced having a tooth drilled (she thought there was no nerve close to it apparently so I asked to chance it) without it entirely and this time it didn't hurt. She said even she wouldn't have been brave enough to do that xD This is coming from me, someone who once held onto the house door handle and had to be dragged into the car to go to the dentist xD so you can overcome your fear if I can.
What helps sometimes is thinking of that woman that has to do the suctioning. If you choke or react badly, it makes her look like she isn't doing her job right and I don't want my cowardice to reflect badly on her.
So to summerise - get a nice person as a dentist, ask for injection to be slow and up into gum (and if you think you can risk not taking it, do so, if that is it is the injection that scares you). Try to stay calm and not get worked up before the appointment because the fear is actually the worst part. And think of the poor girl (usually) who has to suction mounths for a living and focus on making her job as easy as possible.