How can I get my picking hand more smooth? It feels rigid and It's like I'm stressing my hand when I play. I'm relaxed and everything, but its just... messy I guess.
Practice playing scales picking every note. Play on a clean tone and make sure each note rings out clearly. And Obviously play along to a metronome starting slow and gradually speeding up.
You might try warming your hands up before playing to loosen up the muscles. A lot of times I've found I'm tensing up but consciously still try to relax.

What I do sometimes is while I'm washing my hands, (because I always do before playing) I'll run some warm water over my hands. I also gently stretch my fingers apart to loosen up the "webbing" in between each finger and also stretch my wrists.

This usually leaves my hands feeling really warm and nimble which also allows me to relax a little better. Check it out a couple times and see what you think.
Danny L. Small