I hope I'm not too late to add some possible helpful advice here.
There are some people (I'm one of them too) who do not respond to the regular freezing they use at the dentist's office (Lidocaine). I'll explain the reason below in a bit of detail, but if you just want a solution to the problem, ask your dentist to use the alternative freezing agent called Articaine (it'll have various brand names depending on your country, but the dentist should be aware of this one).
In very recent years, researches have pinpointed a disorder called Hypokalemic Sensory Overstimulation. I'm not sure if I can put a link here, so if you just look it up on wikipedia, you'll get a full description. Basically, a person with this syndrome can easily have their senses overwhelmed which can cause all sorts of difficulties (might even feel like a panic attack). These people also do not respond well to Lidocaine during dental procedures, however they do respond to Articaine.
Hope this helps!