Are you feeding her in plastic or glass/metal bowls? Plastic bowls may cause
this. Also, regular cleaning of her dishes and having fresh water at all
times.

My ex-cat Tiggypuss developed a patch of 'geriatic acne' on his chin when he
was about 8 or 9 years old.  I took him to the vet, who gave him very
effective treatment (probably antibiotics, but it was 16 years ago so memory
not perfect).  Tiggypuss recovered very well.

When he was about 18 years old, he developed a sebaceous lump within the fur
on his back.  Naturally, I was concerned that he might have a tumour.  The
vet handled the lump and showed that it was not attached to the flesh of the
cat, but 'floating'.  Literally, just a small lump of fat under the skin.
I'm telling you this in case your cat continues to produce excess sebaceous
matter and, one day, grows a lump like Tiggypuss's.  It's very worrying, and
I wish I had known that these fatty lumps could occur.  If this should
happen to your cat, *of course, take her to the vet* just to be sure, but
don't assume it's a tumour untill you're told.

Just to finish the story, Tiggy lived to the ripe old age of 22 yrs, still
with his sebaceous lump.  It was kidney failure that finally parted us.

Do take your docile lady cat to the vet for treatment, as this acne is
obviously irritating her.  Hope she's soon well.
Spider

An allergy to mosquitos can also cause these types of sores around the
face - particularly the end of the nose and chin. A cat severely
allergic to mosquitos will scratch until it bleeds.

...just a thought.

Troy.

Do you use plastic food or water dishes?  This can be a cause of feline
acne.  My cat had it quite bad but once I replaced the plastic water bowl
with ceramic it has never come back.