I was a pitcher my entire life growing up, and I also played lacrosse, so I was constantly using my elbow. Once my sports career was over and I got into bodybuilding, I noticed how severe my elbows hurt when I did the exercises you speak of.
I went to a sports medicine doc and he did exploratory surgery. He said I had some cartilage build up that he scraped away. He also stated that I have tendinitis, which I think almost any sports medicine doc is going to say with joint pain.
After the surgery and months of rehab, the pain returned and I said, "that's it....I am finding the best doc in my area." I went to the Philadelphia Hand Institute who operates on most of the professional athletes in our area and they said I have a condition known as OCD (Osteochondritis) and the surgery to correct it is very involved and the success rate is not all that great. I opted to avoid surgery again!
Then, I started taking fish oil supplement pills along with Glucosamine Chondroiton, a joint supplement. It has worked miracles, I train today with hardly any pain.
If it does start to hurt, I simply stay away any exercises that bother it. If it hurts bad, I may take a week or two off with absolutely no lifting whatsoever. Too many people try to lift through pain and it only leads to more severe injuries.
I would def. find a great doc in your area and get it checked out. However, if surgery is his diagnosis, I would try the supplements first and see if they have any affect on you. I have recommended it to many individuals and some have had great success with it while others have had none.
Good luck!