Reading your text reminds me of my first of 6 iritis attacks 7 years ago.
Many doctors have no clue as to how difficult it is to put in drops.
After putting in many many drops over the years I have a system that does help. I always try and carry tissues with the eye medication and try to go to a washroom with a mirror if at all possible. Clean hands are the absolute best way to go, but the tissues can help when a washroom is not near where you are. I uncap the bottle and tuck it in my last fingers if there is no place clean to put it down. Then looking straight ahead I line up the tip of the bottle with the pupil of the eye just in front of the eye.