Hi there. The above is pretty good advise. Generally speaking Tendonitis is the inflammatory period following an acute tendon injury. A good way to tell if something is inflammed is if there is a build up of fluid, and excessive heat generated in the injured area.
Seeing as you've had this for about two months, and you claim it is agrivated by Bicep Curls only, then I would assume that this is Tendonosis of either one or both Bicep tendon insertions (into the Ulna and Radius respectively). Obviously take a break from curls, and anything else that agrivates the injury. Don't however completely stop working out. Keep training, as increased metabolism/recovery rates/internal heat/etc, etc, will aid in the healing process.
Like the guy above said, there is plenty of evidence to suggest that eccentric training can potenially promote tendon repair. It's known to be effective even in the elderly. Obviously it shouldn't hurt. For rehab purposes you shouldn't be going heavy, and it shouldn't cause major discomfort.
Good luck man, keep us updated.