How to hold a pen (or pencil) properly and write without pain [8:41]
Summary:
No right or wrong way to hold a pen/pencil, choose what's most comfortable to you. However, if uncomfortable, try changing to a tripod grip, with pen resting on middle finger and lightly held between index finger and thumb. If you use this grip already and experience pain, be mindful of your grip, stop as your hand tenses up, start again and practice maintaining a relaxed grip.
I'd also recommend other videos from this channel as they go into a lot of detail on another handwriting method that can help reduce fatigue. See their playlist, Fundamentals of Arm Writing.
For another perspective on the same topic, you can also check out the video, Practical Penmanship: Fundamentals | Grip, Posture, Muscular Movement.
A lot of the posture advice is roughly the same as with standard typing posture advice (feet flat on ground, no slouching in seat), so if familiar you can skip around those to the details on grip and muscular/arm movement.
Lastly, and somewhat curiously, neither of the individual videos above mention this as much (that I recall in the case of the first), but some simple, basic advice is: take a few second breaks when writing at length and stretch your hands or arms.
Also if you're having trouble relaxing your grip, don't be too proud to get or make grips to put on your pens, if they don't have them already, or pencils. This video mentions these tips, including making writing grips with some tape or rubberbands to help.
Amusingly, I found my way to the first person's videos in part when trying to find advice on drawing without discomfort, but it turns out it's just as applicable, given handwriting is itself a sort of drawing.
Hope these guides and tips help anyone that's been going back and forth on getting into analog journaling but staying away due to finding writing by hand uncomfortable. Maybe this could be your motivation to get into it, to retrain your method of handwriting!