The natural anatomy of the eye allows for our tears to drain into the nose through two small tubes (canalicula) which are connected to the lacrimal sac. Canaliculitis refers to an infection of the tubes that connect the eye to the lacrimal sac. The most common cause of canaliculitis is a bacterium called Actinomyces israelii, but other bacteria, fungi (eg, Candida albicans), and viruses (eg, herpes simplex) may be causative. Symptoms and signs are tearing, discharge, red eye (especially nasally), and mild tenderness over the involved side. Canaliculitis can be differentiated from dacryocystitis. In canaliculitis, the punctum and canaliculus are red and swollen; in dacrocystitis, the punctum and canaliculus are normal, but a red, swollen, tender mass involves the lacrimal sac.
Treatment includes irrigation of the canaliculus with antibiotic solution, and removal of any concretions, which usually requires surgery. Antibiotic selection is usually needed to treat the infection, and the application of warm compresses has been shown to help treat these infections by expediting recovery and minimizing the symptoms from the inflammation. There is no real literature about the best frequency of heat application, but in general, eye-presses may be applied every 3-4 hours until symptoms improve or resolve. The following reputable links all present detailed information and literature about Canaliculitis and guidance regarding how to best treat it with warm compresses: American Academy of Ophthalmology
The Merck Manual