I can't get rid of this tension in my picking hand. It's so bad it makes playing impossible. I've noticed that with big strums it's not a problem, but when I'm trying to pick on one or two strings the tension locks up my picking hand almost instantly. I've tried stretching, I've checked my posture. I've had other guitarists look at my picking technique and they say it looks fine.

I just can't figure out how to make my arm relax. I just don't get how you make your muscles stop doing something.
keep your wrist loose and focus on using as little movement as possible while picking. Try to do that while feeling comfortable and make sure not to use your elbow or whole arm to pick, but the fingers and the wrist.
Remember toi take breaks and don't play in way that makes you tense or uncomfortable.
If you find it painful or impossible to play, you should go see a doctor.