Some opthalmologists are very skilled at injecting BOTOX. Please realize that the husband-wife team of the Carruthers discovered the cosmetic use for this agent. The female half of this team is an opthalmologist and was using Botox to treat blepharospasm. She noted it smoothed out wrinkles, summoned her dermatologist husband and the rest is history.
I really do not know much about opthalmologist and fillers. Fillers strike me as more of a skin thing than an eye thing, but now adays who knows.
Incidentally, let me brag a bit on American medicine. My mother, who helped isolate Botox with Ed Shantz et al back in the 1940's, had a heart attack early Tuesday AM. Back when I started medical practice, diagnosis would have been delayed. Her CPK-MB was normal and there were no changes on the initial EKG. A More sensitive test, troponin , picked up an early myocarial infarction, she underwent an angioplasty and the next day ( today) was sent home. Almost routine. Kudos to her physicians and the technology that lead to the ease of this treatment.