Once you realize that you really need 3 hands, 2 to spread the eye lids and one to squeeze the drops into the eye, you either get a friend to help out, or you struggle on your own. You waste a lot of eye drops by doing it yourself, but take one hand and get that upper lid up, and then put drops in the inner edge of the eye with the bottle inverted above the eye. Don’t have the bottle level with or below the eye ever… Or try pulling down the lower lid and putting the drops in it. Either way, you do not squirt as you say. You put the bottle close to the eye and squeeze a few drops into the eye. Bottle should be facing downward so you get some drops in the eye.
Best is to have a 2nd person hold the upper lid up and lower lid down while you put the dropper close to inner corner and drop in a few drops. Every 4 hours usually. You do not need for horse to hold head/eye up.
Best is a salve you can smear on your clean hand to just smear into the inner eye. Otherwise buy 2x as many bottles of eyedrops as you think you’ll need to handle the amt that will miss the eye when horse moves head.
I’ve only been doing this for decades!