If tendonitis is left untreated, it could develop into tendinosis, which is a long-term, chronic, and degenerative version of tendonitis.
Also, if you experience any of the following, it could be a sign of another problem that needs more immediate attention. See your doctor if you have
Fever (over 100 degrees Fahrenheit)
Swelling, redness, and warmth
General illness or multiple pain sites
Inability to move the affected area