I, too would recommend going to another vet. I've had conjunctivitis myself and it was a miserable feeling it felt like I had sand in my eyes and once I put in the antibiotic drops it was instant relief. Flushing with a sterile saline solution (found in the human contact lens department supplies) will offer some relief, but almost certainly an antibiotic is going to be necessary, since you mention the discharge. Waiting can actually cause bigger problems and a bigger bill because the cornea can become damaged and ulcerate.
The Benadryl ('dipenhydramine' (children's formula) dosage is 1/2 mg. per pound of body weight up to a maximum dosage of 2 mg. per pound of body weight. Always start with the minimum dose. Here's a link to Benadryl.
http://lowchensaustralia.com/health/benadryl.htm