Keep it simple. Do what you're told when you're told how you're told.
Unfuck your mind; the Sgt is just a Sgt and is there to do a job, which it to train you to the standard. Not to stand over you at night with a bayonet waiting to...right?
Despite how 'behind' you feel, strive to improve on YOUR personal performance. Do things that help you become faster; I don't know what they are, that's for you to figure out.
Don't blame poor weapon handling on anyone but yourself. It's not the Sgt's fault 'you get anxious' is it?
Take some time and think; what is making you nervous, anxious. Figure it out. Then figure out what you can do to overcome it.
Most of my Basic 'went horribly' for me too, and the other 120 odd folks in my platoon, yet here I am 25 years later.
Oh, if it helps you any...I was doing my job last week and was feeling anxious a few times, so feeling the anxiousness isn't a big deal. What is important is that you can recognize what is causing it, and figure out how to get passed it. Learning how you can help yourself perform in abnormal circumstances is part of the training goals.
Take some time, figure it out, and put the plan in place to get past those moments. It could be something as simple as 'self talk' in the moments "I've done this before. I can do this now. First I have to field strip the weapon...NO! first I have to prove the weapon safe THEN field strip it. Safety precautions first. the goal is (1) safety (2) sequence and then (3) speed.".
An example. Good luck and in no time you'll be past BMQ and on to the next phase.
PS - the 'self talk' stuff...do it in your head, not out loud. It didn't work out so cool for Pte Joker when he talked to himself out loud...