Sorry to hear that your horses eyes are having issues. With what you are describing there are a few possible causes. Most often when both eyes are affected, it is associated with a topical allergen or irritant, or a viral infection. This leads to a conjunctivitis where we see swelling, redness of the pink tissue around the eyes, and excessive tearing. We can also see increased nasal discharge associated with increased tear production.
Another possibility is a corneal abrasion to one or both eyes. This can lead to ulceration of the cornea, clouding of the cornea as inflammation sets in, swelling of the eye lids, increased tear production, horses appearing to hold eyes closed, or excessive blinking.
It is important to differentiate the cause because we can treat them slightly different. If an abrasion or ulcer is present on the cornea we do not use ophthalmic ointments with steroids like dexamethazone or hydrocortizone because they inhibit healing. We instead use triple antibiotic ophthalmic ointments to lubricate the eye and prevent infection.
To determine if there is an abrasion or ulcer, your veterinarian can use a fluracine stain dye strip. If there is not an abrasion or ulcer, then we can use ophthalmic ointments with a steroid to decrease inflammation and irritation. Until your veterinarian can get out to perform a stain test, I would use an ophthalmic ointment with no steroid.
You can also cold compress over the eyes twice daily for 10 minutes for the first 24 hours, then switch to warm compresses the following day. You may also use a low dose anti-inflammatory like bute or banamine to reduce inflammation. You should also use a damp cloth to wipe away any excess discharge that is accumulating. During the day I would use a fly mask as insects can be drawn to the discharge and will only make the inflammation and irritation worse.
You can check your horses temperature to see if he is running a fever which would suggest a viral infection. The normal temperature of an adult horse is 98.0 - 100.8 F. I also recommend having your veterinarian out to determine if an abrasion or ulcer is present to then provide appropriate treatment.
I hope this has answered your question fully. If there is anything I can clarify or other questions I can answer, Please do not hesitate to ask.