You describe what MANY people experience. It is a form of tendenitis, and will never completely heal. I blew both of my elbows at the same time after years of doing HEAVY(110lbs at 170 lb bodyweight) seated two hand dumbell extensions.
There are however many other excellent tricep exercises.
1. Take a bench and place it in front of the low cable pulley machine. Take a tricep bar and attach it to the cable, lay down with your head near the rack and lift away. It is basically the same movement as a "nosebreaker", but takes a great deal of the pressure off of your elbows due to the fixed position. Works great!
2. Same exercise as above, but with a inclined bench.
3. Close grip bench press. Hands should be about 6-8" apart, NOT right next to each other. By putting the hands next to each other, this places undo stress on the joints. Do this excercise slowly and you will get a great burn.
4. Cable pushdowns. Proper way is to slightly bend the knees, lean slightly forward, and pressdown from the horizontal position with a lock out at the bottom. Do not come up past horizontal. Once you do, it brings the back and shoulders into play. You are working triceps, right?
5. Dips, Dips, and more Dips. Weighted of course.
6. Triceps pushdown machine. If available. This is the one that you put free weights on. Stack some weight on the machine, sit down and press away. You can vary hand position during the set giving you the benefit of 2 or 3 sets in one. You can also do this excercise one handed.
This should give you a good starting point. nd the most important thing to remember is FORM, not weight makes you grow.