I will share this technique that I got from Nicky's eye specialist (multiple corneal abrasions). Take the cap off and put just the metal tip of the tube into hot water for about 10-20 seconds, just enough to liquify the ointment in the tip. I stand behind Nicky and clamp her chest between my legs, bend over and hold her head with my left hand and with the right hand holding the ointment, push the lower lid down and squeeze a drop of the liquid ointment into that space. It flows in and covers the eye evenly, not a big cold clump that is hard to 'drop' into the eye.
A few months ago I got a mild corneal abrasion, and used Nicky's ointment during the night. The next morning I tried the heated trick and what a difference! It felt wonderful, like warm velvet on my eye. I vowed never to get lazy with her eyes again, always take a few seconds to dip the tip in very warm water!
Good luck, I'm glad it was not serious.