Hi. I have had the same problem through the past 6 months. At first, I was pretty stubborn to fix the problem. I thought I could work through the pain and it will eventually go away. I have read tons of articles online about elbow tendonitis, and after reading I realized that the only way to heal it is to REST it. Training through the injury will only make it worse, and could cause permanent damage.
Over winter break, the pain got VERY bad. Every time I picked up a dumbell I felt excruciating pain in my elbow. I decided to stop being stubborn, and I rested it for 2 weeks. After two weeks, I hit the gym again but lifted light for about a week. Its been three weeks now since I returned to the gym and my elbow feels great.
I have read that icing 15 minutes on and off every night is helpful. Also, a number of websites have information to help strengthen the elbow tendons. However, I did not do any of those excercizes, and I still recovered. I have also read that bench press and skull crushers put a lot of stress on the elbow tendons. I still continue to do bench press, but as for skull crushers, I try to stay away from.
My advice is just try to stay away from the gym for at least a week to a week and a half. When you return, STRETCH and WARM UP before you begin your workouts. Also, when you workout make sure you are not trying to do the same weight you were doing when you began your gym vacation. Lift light.
Hope some of this helps. Good luck!