Snuffles. Caused by bacteria, most commonly staph or pasteurella. It is extremely contagious and an infected animal must be quarantined immediately and treated with a safe antibiotic. It can often be severe enough to be fatal. Antibiotics used can sometimes turn out to be even worse then the disease itself so discuss all possible side-effects and reactions the rabbit could have.
I learned about this disease going on 2 summers ago. After helping neighbors get a litter of domestic born wild rabbits out of a field prior to people coming in to cut hay, there was one who took off and never let anybody anywhere near it. I was raising it's siblings while the neighbors were moving as they asked if I could keep them until they got settled in their new place. About a month later I saw this rabbit again then spent close to a month getting it to trust me. Went out every day at the same time rain or shine, and laid out different foods and treats then sat in the grass for 1/2 hour and eventually the time came Zagnut (Dixie Cup, Bon-Bon, M&M, and Snickers were it's siblings) trusted me enough to come right out next to me while eating. The next day I caught him and noticed a sore on him that I believed might be a rat bite. Almost a perfect circle with very thick white pus coming out. He spent the night in a cage outside and in the morning I drove the 45 minutes to the rabbit vet.
The vet examined Zagnut then the wound, and told me Zagnut had a disease called Snuffles. Told me when he saw the pus in the wound he began checking for Snuffles. Further told me that one rabbit with Snuffles can wipe out an entire colony or breeding population. Said if I'd had him with the other rabbits most likely they'd been infected. Thankfully at the time everybody else remained healthy and I was so glad I didn't put him in with his litter mates. I figured being out in the wild he had fleas and didn't want them in my house especially not with 4 rabbits, 2 cats and a dog in there. Vet told me Snuffles has no cure and that there was medication that calmed the symptoms but there was nothing that made it go away and since it's bacterial a rabbit with it should not be anywhere near another rabbit ever again in it's life. Then told me if I had no place for Zagnut to go the kindest thing to do was euthanize him. I asked about just letting him go back and live in the wild and the vet said it would be putting Zagnut through a slow painful death.
I talked with two people I knew who'd had rabbits and they both concurred with the vet. So when my attempts to find him a home went nowhere I allowed the vet to euthanize him. It was not an easy decision. I felt horrible no matter what the vet said because Zagnut was just a baby and it'd taken him so long to trust me and in turn he was put in a cage, poked and prodded then sentenced to death. But I had 3 baby rabbits in a cage in my living room and a 3 year old 2.2lb dwarf Lionhead rescue who'd been litter box trained and set loose in a rabbit proofed room of his own since I brought him into my house when he was maybe 2 months old.
Good luck and I really hope your rabbit isn't this sick.