I usually write 2-3 A5 pages a day, so writing 5+ would make my hand a bit stiff. If you write less than a page a day, you may want to take it easy at the beginning. For example, try a 5 minute journaling practice.
Grip is very important (saying as a leftie who uses fountain pens). You may want to look at a pen like Lamy Safari that has a grip that forces you to hold the pen correctly. Don’t use thin pens like Parker Jotter unless you have really petite hands.
As @mellow suggested, using a pen that flows well is necessary but not sufficient to ease the pressure on the page. If you are a heavy writer, it will take some effort to break the habit.
1. Before getting a new pen, you need to train yourself to write lighter. I would suggest practicing with a 0.5mm mechanical pencil; the lead will break if you push hard. When I first did this, I broke the lead at least once per sentence.
2. Try a few gel and/or rollerball pens. They tend to lay down ink with less pressure than ballpoints. Fountain pens do so as well, but tend to be more expensive and require more maintenance. I bought maybe a dozen different recommended rollerball and gel pens that were under $5 each, tried them out myself and then loaned them all to friends. We each liked different ones the best but liked all of them better than a cheap ballpoint.
as others have said, holding the pen in the correct way, with the correct pressure should help
larger pens/ pencils seemed to help
If you find that your hand hurts even when writing with a pencil, maybe you're gripping it too tight.
Anecdotally, I did go through a a few months of not writing anything by hand, and it did feel weird when I wrote again. Using a regular HB pencil for a while helped.