Could be any number of things. If you've previously been able to do barbell curls without this forearm pain, then my best guess would be that something happened to your forearms along the way. You might have strained them or they might be overly fatigued and inflamed. Either way, I'd recommend that you rest them for a little while. Don't do anything that aggravates that area. After a while, you can ease your way back into doing curls with light weights, gauging yourself to see where you should go from there.
If it is an actual injury, don't try to work through it, as that will only make it worse. Resting will be your best bet here. If you can find other exercises that work around that pain, then do them. But anything that causes pain to that area should be avoided for the time being.
That's my opinion. Hope it gets better for ya