Hello! Poor bun, I've been following this thread and thought I'd throw in my experiences/thoughts. Freak accidents can happen with any kind of animal, so don't beat yourself up about letting it happen. You are doing wonderful taking care of him and looking for help!
My rabbit never got injured in his eye, but he would frequently get irritated eyes when he got older, and once he got what I believe was either an eye infection or a very bad irritated eye. I used the terramycin that other people are talking about, and it seemed to clear up his eye so quickly! Lion, my rabbit that got it, had red, swollen eyes that didn't have the discharge from your bun's wound, but they would water a lot. The terramycin helped a lot in my experience.
I saw other people mentioning the chamomile tea bags--again, this is something I used to use all the time with my rabbit Lion when his eyes got irritated. Somebody on BYC actually first mentioned it to me, and I found they always worked really well too. I would heat up some water in a mug and let the tea bag sit for a minute so it was warm, but not too hot, and then I would hold it on his eye/s for about ten minutes. I honestly can't remember if it was only once or twice a day, but at least once a day I did this, depending on how bad his eyes got.
I know other people are mentioning using triple antibiotic cream in the eyes--I have zero clue myself how that would affect a rabbit, but at my barn we use triple antibiotic cream in the eyes of our horses who get irritated eyes from sand/heat/flies. It always clears their eyes up wonderfully. We usually apply once or twice a day depending on how bad it is. A rabbit is a ton more delicate than a horse, though, so I can't say what it might do to them.
In my opinion, as others have said, I'd use terramycin if you can get it, and the chamomile tea bags--warm and damp, not soaking wet. After washing, I'd use either a towel or paper towel to very gently dry around your bun's eye the best you can. If it remains really wet from water/tears, it can create hair loss and further irritation to his skin around the eye.
Best of luck to your poor bun! I hope he makes a full recovery soon.