My guess is your training to heavy and moving the weight around.. Been there done that and couldn't bench press or work triceps out for a couple weeks.
Now I primarily train for sarcoplasmic hypertrophy .. My elbows and joints feel great .. Sure I'm not tricep pressing 225 anymore , but who cares..
Here's what I've been doing -- instead of doing rope pull downs with 170 pounds, I drop the weight all the way down to 70 pounds. . Before I begin the movement I flex the tricep muscle hard, I then keep the tricep flexed hard the whole movement,, take 2 seconds to push down, hold it flexing hard at the bottom, and keep flexing and go slow on the negative (like 5 seconds)..
Don't just move the weight from point A to point B-- Flex and work the muscle slowly during the whole movement.
You'll get way more time under tension, a better workout, and NO joint pain