Usually when you buy from the pet shop it will indicate on the bottle or the packaging for the correct dosage for your cat.

To clean your cats eye, please wet a facial cotton with water.
Then press excess water out from the cotton and then slowly wipe the cats eyes.
Slowly pull open the eyes and rub inside too.
After doing that use another fresh cotton wool for the other eye.
Do not use the same cotton wool for the other eye.
After cleaning, put some eye ointment on the sore eyes.

Did your vet give you any eye ointment for your cats eye?

Usually eye ointment works more faster than eye drops.
Eye drops you will need to put once in every two to three hours.
If you are working then it will be difficult.
If eye ointment you will need to put only twice a day.
Yes, I know what you mean.
I feel scared too as I don't want to hurt them when I pry open their eyes but its for their own good.
That's why use a wet cotton wool to clean and once the eye area is wet its easy to pull open the eyes.
You are most welcome.