AWW, Poor Boo.
I’m going to tell you what helped my cat who had similar chin/nose problems – vet said it was acne & needed antibiotics & face washing each time it reoccured.
The antibiotics were always for 10 to 14 days & vet said it should clear up before pills are done but finish pills anyway.
It always took 3 weeks for it to clear up.
He started throwing up the antibiotics so I decided to try not going for the pills & to only was his face – healed up the same 3 weeks so no more pills for us.
His face was washed during outbreaks only.
Once per day with Hibitane skin cleanser – people soap, the same pink stuff that the vet uses – rinse very well & keep away from eyes – I would ask the vet if this is rabbit safe 1st.
3 or 4 times per day holding cotton balls dripping/soaked with peroxide against scabby areas.
I read somewhere that plastic bowls can house the bacteria so I switched out all food & water bowls to glass/ceramic ones & would spray straight vinegar in them everyday to clean them.
Like bunnies, cats chin mark things so I thought he may be spreading the bacteria around & then reinfecting himself so during outbreaks;
I would squirt all the upolstered furniture down with vinegar every 2nd or 3rd day.
I would wipe all the hard surfaces down with a peroxide soaked rag – check for finish damage in an unseen corner.
I tried to keep the litter box clean & wiped the chinable edges often with peroxide.
I also read that it could be food allergy or stress related.
I could never really figure out if it was food, I switched brands but it would come back eventually.
Today there are more options for cat food.
Bunny food is a lot like cat food then – all very similar ingredience – corn is a big animal allergen though so check for no corn.
Trying a different brand can’t hurt.
New litter box maybe – bacteria could be lurking in the scratched or chewed spots.
Try a different litter.
Soak/clean or replace brushes or combs.
Since the meds are not working very well, I’d be trying to think of all other possible causes.
Could it be a household cleaner – try a different one.
Could it be a furniture polish – try not using one for a few weeks.
Could it be your laundry soap or fabric softener
Could it be something in the tap water – try filtered or bottled for a while.
Could if be the furniture fabric – toss a blanket on top or try to keep him off for a while
I’m just throwing ideas out there.
By the way, I had 2 cats & only 1 ever had the acne problem & it would reoccur every 6 months to a year – for his whole 14+ years.