Here are my thoughts, for whatever little they may be worth to you.
Your instructor is not going to allow you to get hurt or ask you to do something that is likely to injure you. The key to all of diving is to stay calm, relax, solve whatever challenges you are presented with in the water (not by bolting to the surface), and simply keep breathing.
If you go into the experience knowing that diving is easy, millions of people with no extraordinary powers or latent talent do it every day, and anyone that can keep breathing and chill out can likely handle anything PADI teaches, you'll be fine. You are going into the water with a paid professional who makes a living teaching diving to normal people. Even if you close your eyes (perhaps when taking off your mask during one of your skills), they are still right there, watching you and ready to assist you if needed.
Just keep breathing. In and out. Nice and calm.
In recreational diving within no decompression limits, depth is your friend. Buoyancy control is easier at depth. I'd rather be at 20M than 3M - everything goes more smoothly at depth in my opinion.
Final thought.... you are learning how to be a DIVER not a FLOATER. When you learned to drive a car, you likely didn't jump out of the car any time something challenged you. Likewise, you should try to face situations in the water and not seek out the surface as some magical panacea. Drivers don't learn to drive by getting out of the car, pilots don't learn to fly by jumping out of the airplane, surgeons don't learn to operate by running out of the operating room, nor should divers look to the surface as a solution for things they can easily resolve underwater.
Be calm. Keep breathing. Slow is smooth, smooth is fast. You've got this.