Hey Dan,
You should send a video in of you picking so we can see what your technique is like, but here are a few tips that really helped my picking:
1. Make sure you're not squeezing your pick. A tight squeeze on the pick can end up contributing to arm tension. You'll want a really relaxed grip on the pick so that your wrist is loose,
2. Make sure you're picking from your wrist (mostly) - If you find that you use your forearm rather than your wrist to pick, this will definitely cause it to tense up and be rigid, as it will need to make rigid movements to pick a thin string, because it's a big limb.
3. You didn't mention speed specifically, but just in case that's what you're looking to get going, make sure that with all of the above, that you're really ready to try and pick as fast as you are - as if you're trying to push yourself to go faster than you're capable, that will also cause unhealthy arm/wrist tension & lead to rigid movements.
Basically, in order to have a healthy picking technique, it needs to be both relaxed & controlled (i.e loose but not sloppy) Try sitting with a metronome as a really slow speed & use all of the above tips - keep relaxed & keep your picking from your wrist, really controlled, kinda like if your hand was a robot hand. If you start to feel any tension, immediately stop, take a sec and jump back in. Be really strict with it.
The biggest piece of advice I can give for picking, is to remember that when your brain tells you you're ready to go faster, it is 100% lying to you! - When you hear that voice in your head, stick to where you are and practice the controlled relaxation some more. I feel like a lot of guitarists, myself included have this inner 'speed gollum' that's just dying to get their hands on the technique they want, straight away
Patience is key!
Hope this helps!