If you can take the AOW class before your trip you'll learn a lot about buoyancy control. That was the #1 benefit my wife and I both received from the class. We only had five post-OW dives when we took AOW, but we could have easily taken it immediately following OW.
Sure, during the AOW class we did five intro dives to five different specialties, including peak buoyancy, but the instructor focused on buoyancy on each of the five dives. By the time that weekend was over our buoyancy control improved dramatically.
Anxiety/panic? Anxiety comes first. Then panic. How well you're mentally prepared will determine the progression between the two.
If the anxiety is caused by rapid breathing and CO2 buildup, you have to calm your breathing to reduce the CO2. CO2 causes you to feel anxious and to breathe faster. Don't; it just makes the anxiety worse. Breathe slowly and deeply from the diaphragm (belly should poke out when you inhale). You should feel very relaxed during a dive. Try it while you're reading this. Think calming thoughts, breathe deeply and slowly from the diaphragm, pausing briefly between each breath, and feel how relaxed you get. The same thing works underwater.
My wife and I watch each other's bubbles when we dive. If we see the other person breathing shallow and rapidly, we get the other's attention and give them a "relax" signal. Hold your hands out in front of you like you're praying, then slowly push them down and out, like you're running your palms over a table top. That's our signal to relax. I've even seen my wife do it on the dive boat with her eyes closed just to help herself relax.
If the anxiety is caused by just being underwater in a foreign environment, my suggestion, born from years of instructing pilots, is to visualize EVERYTHING in advance. There are so many parallels between diving and flying it is amazing.
Make a list of the parts of a dive profile when you feel the most anxiety. Then dive that profile in your mind. Find someplace quiet, relax, close your eyes, and visualize the entire dive. If need be, start with suiting up and and mentally work your way through an entire dive. Visualize everything in your mind until it becomes as familiar as being there and doing the dive. Feel the water, hear the bubbles, feel the regulator in your mouth.
When you get to the part of the profile that gives you anxiety problems, feel the anxiety, then solve the problem in your mind. Figure out what is causing the problem then find a solution to quiet the feelings, replacing them with calm. Maybe it is your breathing, a leaky mask, poor buoyancy control, gauge surprises, fatigue, muscle cramp, bad visibility, big fish, disorientation, loss of buddy, mismatched buddy, whatever. Visualize whatever is causing the anxiety, take control of it, resolve the issue, relax, then continue the dive in your mind. Repeat the anxiety profile and its solution as often as necessary until it doesn't bother you.
And no matter what............have fun.