My cats eyes have black discharge

I recently adopted a Himalayan cat, Steve, and he's been battling upper respiratory issue ever since. He came to me with fleas, and ear infections in both ears, congested. We took care of the fleas and ears but I've had a constant battle with his upper respiratory issues, Which has kept me from being able to update his shots. He had been sneezing, and having yellow discharge from his nose and I would hear him having a Hard time breathing. When I picked him up from the shelter I adopted him from, they gave me a course of clavamox to give him morning and night for 10 days. It seemed to go away but soon came back so I took him to the vet, explained all of this and he gave me another course of clavamox. Again it went away and came right back, except now there is thick black discharge in both eyes in addition to the other symptoms so I took him back to the vet and he gave me a course of a different (hella expensive) antibiotic called orbax and told me to start giving him half a Zyrtec in the morning and at night as well. We just finished the last day of the orbax and his congestion seems to be a little better but there is still thick black discharge in his eyes. I'm taking him back to the vet but wanted other opinions. He's grooming himself and eating and drinking really well but doesn't seem to be doing well until I've been home from work for an hour or so. Steve and I are both really tired of expensive vet visits and he needs to get better so he can get his shots! Anyone have any other input about what is really wrong or what will help? I would certainly appreciate it

are you giving him lysine?

Not yet, I just found out about it while researching online but my vet didn't say anything about it and Was unclear exactly when it was appropriate to do so. When should it be used, and how often/how much?
Thanks for such a quick reply!

"Oral supplementation in cats with 250–500 mg of l-lysine  daily (often placed in the treats) may reduce the severity and frequency of recurrence of FHV-1 conjunctivitis and keratitis."

http://www.merckmanuals.com/vet/eye_and_ear/ophthalmology/conjunctiva.html?qt=lysine cat&alt=sh

you can get it in different forms -- powder, treats, etc. 

there are a lot of catsite threads on this topic. just do a search. 

Thanks!