Ipod1, really hate dental work here too!!
Just wanted to tell you, in my experience, being numbed for dental work on bottom teeth has never rendered me unable to swallow.
Two root canals & 5 fillings on bottom teeth & no problems swallowing. This work was done by 4 different dentist & still no problems.
To feel better about this call or have someone call your dentist office & discuss your concerns with him/her. I panic too, have to take Ativan to get thru but have survived. My hunch is you'll be fine though.
Best wishes.