I'm late to this party, but here's my take on it. I choose to dive in high currents so am used to it.
1. Surface swim with snorkel: I only ever use one when required by standards. The DM (my guess) instructed people to keep a snorkel in to prevent them getting a mouthful of water. I personally keep my reg in, but on the surface breathe around it (so loosely hold it in my mouth)
2. I hate surface swims. If I can fin on my back, then just beneath the surface (keeping tabs on the line) Obviously hard to do on a guided group where everyone is moving at different speeds.
3. A decent set of fins never hurts either.
4. Relaxing at the surface, is important - but then holding at the surface can be stressful, being just under the surface and descending slowly while getting yourself together is possibly the best.
5. Problems descending - it shouldn't be, as you should be negative. My guess (assuming you were correctly weighted) is either that there was still air in your BCD - not fully dumped as you made a quick descent. Also, because you were stressed, your diaphragm would have dropped (a reflex) giving you greater lung volume, and combined with heavy breathing made you more buoyant.
6. Breathing hard and fast through reg - I personally hav regs where I can adjust the breathing resistance, I would turn them down to hard if I was over breathing OR I'll restrict the flow by placing my tongue near the mouthpiece (not fully blocking it) This is just to stop the runaway scenario where you breath faster and faster - the breaths becoming more shallow with less O2 and more CO2 retention. Then try to think "happy thought"
The latter isn't' easy, you were clearly outside of your comfort zone and clearly stressed especially at the bow. (I love it when the current is strong enough to make my mask vibrate - hooked on with a line) It's clear as you drifted you regained your composure.
The only way to get used to currents is exposure to them, they can be very unnerving at first because you feel so out of control. When I started, my wife use to make me fin through (what I felt then were) strong currents. I'd use 50% om the air bitching at her through my regs. when I look back to what we do now, my early currents weren't currents at all.
If you are nervous another time, consider a 1:1 Dm so you can take things at your own pace. You'll probably be more mentally prepared next time, but as always if in doubt don't dive. Diving is supposed to be a pleasure