Hi Miranda,
To answer your question....
Does this mean that it is definitely going to involve extraction of teeth with roots in the sinus cavity?
No, not all upper back teeth have roots in the sinus. Depends on the anatomy of your sinuses and the length of the roots of your teeth.

Sinus exposures are not uncommon during extractions of maxillary posterior teeth. They are usually not a cause for concern and can easily be repaired. Sometimes the perforation into the sinus is so small that it just heals on it's own.

There are usually two (rare) situations that would be of concern:
One is if a tooth were severely abcessed and the the infection had invaded deep into the sinus cavity.
The second would be if the root of a tooth were broken off during an extraction and it was pushed up into the sinus.

Both of these situations are rare and not something that you should worry about. If you had an abcess that caused a severe infection into the sinus cavity, your dentist would have already told you about it.

The novocaine shots that you said were painful may have been when you were given an injection in the palate. Extraction of upper teeth requires a palatal injection and they can be a bit ouchy. However, this area numbs up very quickly so the subsequent injections in that area should not be uncomfortable.

The burning pain that you described in the roof of your mouth could have been an irritation in the surgical area from something you ate. Or, you could have developed a canker sore in that area, which is very common after oral surgery for some people.

Have you ever tried homeopathy for pain relief? I have lots of patients who have great success using Arnica, Belladonna, Hypericum, Ruta, or Staphysagria. Each of these does something a bit different and not all are necessary to take. A google search on each of these which regard to dental anxiety and oral surgery pain, could give you some insight into which one may be helpful to you.... if you choose to try it.

Hope this information is helpful to you.
Bryanna