It would be odd to use drops and ointment with the same ingredients.
With a simple corneal ulcer they generally feel much better and the ulcer is well on its way to healing 24-48 hours after treatment is started. So if this was a simple ulcer he should be much better.
Some dogs get ulcer that don't heal normally and quickly. These are called indolent ulcers. There can be indications that this may be an indolent ulcer when we stain the eye. We can see flaps of corneal tissue at the edges of the ulcer rather than a sharp edge that indicate an ulcer that may have trouble healing, or the ulcer may be deep or larger than normal, or he may have blood vessels forming on the cornea indicating the ulcer isn't a simple one.
Since Charlie is hard to examine he may need to be sedated to get the eye properly stained and treated. There may be a foreign body stuck in there that is delaying healing too.
With an indolent ulcer the best chance we have of getting it to heal properly as quickly as possible is to debride the lesion and then protect the ulcer with a temporary third eyelid flap or a soft contact lens.
If we don't treat indolent corneal ulcers aggressively they can turn into a melting corneal ulcer and the eye can rupture.
In some cases dogs have to have an even more aggressive surgery called a conjunctival flap to treat indolent ulcers and save the pup's vision.
If you are concerned that this treatment is too aggressive then you can try using oral nonsteroidal anti-inflammatories for pain and inflammation, antibiotic eye medications to prevent secondary infections and eye drops with hyaluronic acid to help protect the eye while it is healing and keep it moist. He should be rechecked in 5 days and if the ulcer isn't gone or almost cleared then you can decide to go ahead with more aggressive therapy at that time.
But given his slow healing now and dislike of being handled I would probably sedate him, stain his eye and debride it if an ulcer is there to stimulate faster healing. Then follow up at home with oral nonsteroidal anti-inflammatories for pain and inflammation, antibiotic eye medications to prevent secondary infections and eye drops with hyaluronic acid to help protect the eye while it is healing and keep it moist.
In the meantime I would add artificial tears to his regimine. Apply 2-3 drops to the affected eye every couple of hours. The more moisture the better.
Does that make sense? Do you have any further questions for me?