Can sulfamethoxazole /trimethoprim be used to treat conjunctivitis?

Sulfamethoxazole /trimethoprim is not used to treat conjunctivitis.

Treatment of conjunctivitis depends on the cause.
Viruses are the most common cause. Other causes include allergy and bacteria.

Allergic conjunctivitis may respond to allergy treatment. It may disappear on its own when you avoid your allergy triggers.

Antibiotic medication, usually eye drops, is effective for bacterial conjunctivitis.

Viral conjunctivitis will disappear on its own. Many doctors give a mild antibiotic eyedrops for viral conjunctivitis to prevent bacterial conjunctivitis.

You can soothe the discomfort of viral or bacterial conjunctivitis by applying warm compresses (clean cloths soaked in warm water) to your closed eyes.

https://www.drugs.com/health-guide/pinkeye-conjunctivitis.html