I’m not a doctor and can’t give you a diagnosis, but I can give you some suggestions that you can explore with your doctor.
It sounds as if that could be two things going on with you. Your fingers bending could be a sign of damage to the joint that prevents it from moving freely. Are you taking any disease modifying medication for your RA? If not, I’d recommend that you talk to your rheumatologist about the symptoms and so you can explore some treatment options.
Secondly, the locking of your fingers sounds like it might be trigger finger. This is a condition that can happen with RA, in which inflammation narrows the tendon sheath. As this sheath narrows, it makes it more difficult for the tendon to move through it, hence the locking. There are couple of options for treating trigger finger. One is to give the affected joint rest for some time by using a splint. Surgery is also an option. I have the same thing on both little fingers. The doctor says he can fix it with a fifteen minute operation, but I haven't done it. Talk to your rheumatologist about this issue, as well. You may want to try the less invasive treatment option first, but if it doesn’t do anything, surgery may help you.