Here's some info from The House Rabbit Society:
Tearing and Runny Eyes
Rabbits have a number of problems involving their eyes, the most commonof which is tearing or discharge from the eye which we call "epiphora."
Epiphora is a symptom, not a disease in itself, a sign that therabbit's eye is not able to drain tears. Most often epiphora is seenwhen the drainage system is not working correctly, typically when thetear duct is blocked by debris, such as mucous from the tears, or bydischarge and swelling caused by infection in the duct.
Less commonly, epiphora occurs when too many tears are produced for the system to handle (as when a person cries).
The rabbit's tears drain from the eye through a single opening in thelower eyelid called a punctum or plural puncta, located in the medial(nose) side of the eye, nestled in an indentation in the lacrimal bone.The upper portion of this duct forms a funnel-shaped chamber called thelacrimal sac. The lacrimal sac collects tears and directs them down thecurving course of the lacrimal or tear duct, through the bones of therabbit's skull.
There are two locations where the duct narrows or flattens: at themaxilla bone the diameter narrows, and as it passes over the roots ofthe upper incisor teeth the duct is significantly flattened. The ductopens at a nasal punctum, depositing tears just inside the nostril.
The narrow and small diameter sections of the duct may become cloggedwith normal mucous discharges from the eye or debris that hasaccumulated in the eye. Other causes may include trauma to the lacrimalor maxillary bones of the face and impaction or abscesses of the upperincisor teeth which further constricts the lacrimal duct.
Disease of the lacrimal sac and duct is called dacryocystitis.Dacryocystitis is most often secondary to bacterial infectionsoccurring within the duct. Surprisingly, most of these rabbits do nothave infections of their eyes. Pasteurella multocida bacteria is themost common cause (making dacryocystitis part of the "snuffles complex"of upper respiratory disease seen in the rabbit). Staphylococcus sp.and Streptococcus sp. are also commonly found.
Diagnosis of dacryocystitis is based on clinical signs, cultures of thelacrimal duct and on cultures and cytology (microscopic examination) ofmaterial flushed from the duct. Radiographs (X-rays) of the rabbit'steeth and facial bones may also be indicated.
The importance of performing diagnostic tests varies with the severityof the case. A rabbit who has no prior history of tearing problems andhas no pain, swelling or redness of its eye or area over the lacrimalsac, and no signs of infection of its eye, very often will respond toflushing of the lacrimal duct and topical medications. Rabbits with ahistory of repeated problems with tearing should have a more thoroughset of diagnostic tests performed.
Treatment of dacryocystitis is aimed at opening the lacrimal duct andcorrection the underlying cause. Typically this includes both oral andtopical antibiotics (eye ointment or drops). If the eye is infected,that problem must be addressed as well. Rabbits with dacryocystitisoften have tear scald (much like diaper rash) caused by tear drainingonto their face. Correction of the tearing helps to correct thisproblem. However, many rabbits will benefit from shaving the hair overthe affected area and application of a topical medication to reduce theinflammation and aid in healing.
It is difficult to correct dacryocystitis in rabbits with underlyingchanges of their facial bones and/or abscesses of their cheek teeth.Palliative measures may need to be initiated to make the situationbearable during the long course of treatment to correct the problem or,in some cases, for the rest of the rabbit's life. These may includetreatments aimed at preventing tear scalding of the face or evenmedications or surgery to reduce the amount of tears the eye produces.
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I would highly suggest a vet visit when you can afford it (but I cansympathize, as I know what it's like to have a sick animal and no fundsfor the vet), as the cause could be from many different things. In themeantime you could try bathing the corner of the eye with a mildsolution and continue isolating him, as well as continue handling yourother rabbits before touching him, and washing your hands well afterhandling him, at least until you know the cause. Hopefully it is simplyan irritant, or a blockage in the eye duct.
