It sounds like you need some confidence in the water at the moment - have a word with your instructor or DM about expanding your dives (PS in my experience there is really not much difference between shallow and deep dives apart from you go through air a bit quicker, they may be a bit darker and you might experience being narked - I can't say I have felt it though).
I try to remember that any time I get a little stressed underwater (it happens to everyone), slow down and take a slow deep breath. The only thing that is an emergency underwater is lack of gas (which you should be keeping an eye on) and that is where your buddy comes to the rescue. Anything else and you have plenty of time for action - Stop, Breath, Think, Act.
With regards to buddies, it is important to get one that you can speak to about any issues - they should not be pushing you to do things you are not OK with. We all have our personal limits and they should be respected. I am OK with swimthroughs (so long as they are not tight and I am aware of the exit) but I will not do cavern/cave dives. Strangely though I am happier with penetrations on wrecks (generally on the popular wrecks I have been on the penetrations have been wide enough to allow assistance if needed).