Well... There are a couple of things to say. I'm sure you've heard it all but I'll repeat it.
1) you're not special. This happens a lot in training but 99% of students get over it. You will learn if you just let it go and let the INSTRUCTOR tell you when it is good enough. What I often see is that the student is putting THEMSELVES under pressure and it makes it worse instead of better. For example, it's common for your breathing to "stutter" at first when you are learning this skill. Some students get frustrated by this because think they're doing something wrong when this happens, they aren't. They are learning. With time and practice, the stutter goes away. I don't konw if you have this problem but the example is to illustrate the idea that if you just focus on what you're doing and not worry about if it's good enough or not, that it gives you less stress.
2) What helps most of the people I've seen with this problem is to realise (a) if you can breathe then there IS no problem and (b) if you plug your nose, then your regulator will just give you air..... ie... you can always breathe. When you are first learning the skill it helps a lot to plug your nose and take a couple of breaths to realise that everything is just fine.... then go to the next step..... There is no time limit for clearing a mask so go slow. I harp at my students about this constantly. To make things easier, go slower.
about #2. A lot of divers and some instructors will tell you never to plug your nose. My opinion about it is that this is incorrect and damaging advice. If it helps, then do it. However you have to realise that you can't always plug your nose so the END (repeat END) result you're looking for is to be able to clear it without this. However, in order to GET to the end result this step is very helpful for some people.
plug and breathe.... plug and breathe.... and then when you feel comfortable, plug for shorter and shorter and eventually not at all.... the END result is sacred. Any technique you use to get to that end result is justified. If you think something will help then do it.
3) Anxiety is often caused by the brain being occupied with thoughts that are completely irrelevant. A meditation teacher I know says that your entire life is just chaining together "the next 2 seconds". I've had good success with students by telling them this. When ever anything happens, just keep your mind focused on the next two seconds and let the rest of it go. Let go of what your husband will think of you if you can't learn this, what the instructor will think, what the other students will think, if your dog will still love you, if you are going to pass down these genes to the next generation.... etc etc... If you have water in your mask then just observe that fact by saying to yourself, "ok, I have water in my mask". (2 seconds). "let's take a breath" (2 seconds) "I need to cough so I'll plug my nose" (2 seconds) "to clear it first breathe in" (2 seconds) etc etc. All of the other stuff is just ballast that gets in your way.
BTW this isn't true of just diving. Have you ever noticed that people who live in the "here and now" are more relaxed, more balanced and happier...... ? I'm not saying you're not, but I am suggesting that the next 2 seconds is all you ever need to think about in order to solve a problem that's giving you emotional stress.
Hope this helps.
R..