I would suggest that you ask your dentist to supply a tranquiliser precription - or if he is not able, then your GP. All you need is one 5mg tablet about an hour before you go, and you'll be nice and relaxed.
As others have said, with modern dentistry, it is highly uinlikely that you will feel any pain. the scratch from the injection lasts seconds, as the freeze takes effect, and after that, nothing. Try to breathe deeply and swallow gently, and you'll be absolutely fine.