Like Cindy I'm am happiest and calm under the water. It is quiet, peaceful and lovely things abound.
I have a healthy respect for the potential dangers of diving and therefore have always followed the rules of diving. Simple things like check your equipment before diving, always dive with a buddy and stay relatively close to them. Hint: a buddy can't help you in an emergency if they are off exploring a different part of the ocean. Follow the rules of descending and ascending from the sea.
To address each of your fears:
Sea creatures that sting, bite and chase--- Most divers wear a dive skin to assist in protecting their skin from those issues. It helps keep you warm but a thin skin is also a safety barrier.
When learning to dive they teach you how to control your buoyancy so you stay off the plants and corals. This will prevent you from getting scratched. In a couple of hundred dives I have not encountered anything chasing me.
Health concerns-- everyone hears about the bends. It is real and can cause major health issues. If you follow the rules of diving it is extremely rare to experience theses issues. All divers can tell you a horror story about some dude...who did something stupid and got the bends or nitrogen narcosis. Generally following the rules will keep you very safe.
Tempermental dive instructors-- I've really not encountered all that many of these. Most are exceedingly happy, competent and want to make certain you have fun and are safe. If you get a crazy one (unlikley) do go diving with him.
The water does exert a different pressure on your body as you go deeper in the water but you cannot tell or feel it. You will always feel light and free flowing.
When you take a dive class your beginning instruction will be in a swimming pool. You will have time to become accustomed to the surroundings. If you freak out you can stand up. It is a very safe environment in which to learn.
Since you have a few fears to over come selecting a good location for your first open water dive will be important. I did my first dive in the Bahamas. The water was warm, it was a beautiful sunny day, the water was crystal clear. I could see for 100+ feet. I felt comfortable and safe because I could see everything around me.
I know many people who have done their first real dive in a quarry or lake with poor visibility. I don't recommend that. You want to have a pleasant memory and become comfortable with your surroundings.
Mel, hopefully you will decide to become a diver.