This is normal, but I’m betting you’re making the common fretting mistake that most people make. You are probably curling your fingers over the top - claw style - rather than laying them flat on the strings.
My advice is to think like you’re holding a sandwich. Holding a sandwich is what the resting shape of your hand should be. That is also how much pressure it should take to fret. (Don’t stress about this too much now. This will make more sense as you progress.)
Here is a video I made for another beginner that illustrates what I’m talking about with hand shape:
My picking hand is cramping while playing “Come Together”.
I want to play it with a pick and palm muting. I really like that tone. Normally, this is not a big deal. But for some reason, on this song, my hand starts cramping a bit after halfway through.
Thoughts or suggestions? Is it the position palm muting? Just do finger style?
Aha! I think that’s what’s doing it. Using my hand more than my wrist.
Usually, when I’m pick-playing, I’m more strumming alternating strokes. For this, I’m trying to hit those two initial staccato attacks with tight, even downstrokes. That means I’m holding a lot more tension in my hand.
I need to figure out how to get that nice downstroke motion with my wrist, especially while palm muting.
…
Edit: Yup. This was the answer. Still gotta clean up the technique to not miss strings, but on the pick rake up, pushing through the strings with my whole wrist sliding up the bridge so I’m pushing through the strings using arm muscles instead of trying to push through with finger strength.