Abyssal let me start by saying IM TERRIFIED OF THE DENTIST! When I was child I had a bad experience and I've had an extreme phobia ever since. They scare me to death so I feel ur pain. Shop around for the right dentist and don't be afraid to say that u have a fear. Now I'm not sure if ur afraid of the procedure or the period afterwards but both can be managed. Under most circumstances my regular dentist (not my brother in law who I went to cause I needed it done ASAP) will prescribe me Valium to calm me before the apt. Then I get gas and an IV drip of Valium during. You are basically asleep, feel nothing and remember nothing. You just have to find a dentist who uses IV sedation. As far as afterwards goes the vicodin or Tylenol 3 will manage any pain u may have and I've also used a warm heating pad at times. Dry socket is when a clot doesn't form in the space or only forms partially and can be painful but a quick procedure at the dentist will remedy that if it should happen.
Just remember ...divers are horrible with nitros masks. They only cover ur nose and we are used to deep controlled belly breaths and good mouth exhalation. At the dentist it's all bout the nose. Short to normal breaths exhaling through the nose seems to be the key. Otherwise they want to kill us because we keep collapsing the bag in the gas apparatus. LOL even so it's hard to not to go into scuba mode whenever someone straps a breathing device to ur face!
Good luck!!! I'm sure ull do fine

One more thing.. I always stress that I dive and sometimes u may have to explain abit why this is important to ur dental work..trapped air in fillings, anything that affects sinul passages etc. That way they take a little extra care so that u don't need a redo layer.