Elbow Pain after Triceps Training

I have a tough time training triceps because a few months ago, my elbows would hurt a lot after increasing the weight. I tried training triceps with very light weight and would avoid full lockout (which caused the most pain). Now I’ve hit a brick wall - I’m stuck at a fairly light weight (20 reps+) and whenever I increase, my elbows start hurting regardless if I avoid lockout. This happens when doing rope pulldowns and lying barbell extensions.

After training, I ice and elevate my elbows if necessary which usually makes the pain subside after a few hours.

Any ideas how to heal this injury? I’ve stuck with light weight/careful form for a 8 or 9 weeks already. It’s noticeably improved, but will more rest necessarily help?

EDIT: added diagram

http://www.tennis-elbow-help.org/images/innerandoutermuscles.jpg

I’ve heard that using a speed bag as a warm up will help get bloodflow to the elbows and help avoid tennis elbow. I suffered from tennis elbow about 8 months ago, once It cleared up I started using my speed bag before rows, pull ups, bench and overhead pressing and haven’t had a problem since. Some dull aches and pains here and there but nothing like when I had tennis elbow.