Sounds like you may have a rotator cuff injury. If it's the long head (outer) of the biceps brachii that hurts then more than likely it's the infraspinatus and/or teres minor muscles. Exactly the same problem I had.
Read
this starting at the 4th paragraph, it explains it better than I could.
Rotator cuff injuries are very common among weight trainers. The tendons of these muscles are prone to inflammation so ice and anti-inflammatories will help. Try and
see a sports doctor or a shoulder specialist.
The 4 exercises below directly target each of the four rotator cuff muscles. Use the same weight* and reps for all 4 exercises (you want balance). Start with 15 reps then work up to 25 reps before you raise the weight.
http://www.exrx.net/WeightExercises/...lRotation.html
http://www.exrx.net/WeightExercises/...lRotation.html
http://www.exrx.net/WeightExercises/...lRotation.html
http://www.exrx.net/WeightExercises/...eralRaise.html
*When I started doing these I could do like 10 lbs in one exercise but only 5 lbs in another. I adjusted to 5 for all. It's NOT about the weight It's about overall balance. I now do these as part of my warmup and never more than 15lbs.