How do you get rid of wrist pain?

You can manipulate your grip when using barbells or dumbbells. I used to get wrist pain all the time in the gym, but I found ways to avoid it. However, in your case I would simply recommend using an EZ curl bar. You should not be doing bicep curls with a straight barbell in my opinion unless you have flexible forearms. Put your arms out in front of you and turn them in the direction of your thumbs until you experience a little bit of tension. You will probably notice the tension hits you well before your palms are facing the ceiling. This is because you have a limited range of motion in the forearms, and so slamming them with heavy weights is going to cause muscle tears. However, if the pain you’re experiencing is not muscular, and seems to be joint-related, then you should consult a doctor.

Use an EZ curl bar, or dumbbells. The isolation exercises I do for my biceps are concentration curls, hammer curls (which also seem to target the brachioradialis muscles), EZ curl bar curls, and EZ curl bar preacher curls. Do these exercises instead and you should experience much less pain. At the end of my back / biceps day, I like to do 2-4 sets of any of these aforementioned exercises (e.g., 2 sets of hammer curls and 2 sets of EZ curl bar curls).