Sorry for your babies condition.
My female veiled chameleon has very dry eyes, this is what I do, and she understands what I'm doing, she never fights it.
I take water, and add Repti-Safety drops according to directions per cup. I get a paper towel, and get it soaked. I put my hand as close to her eye as she is comfortable with and squeeze the reptile-safe water over her eye.
I try to keep it to a small stream and squeezing slowly.
My Lady Jade will close her eyes, and you can see her eyeball stretching the skin behind the lid.
It's been working since I got her and noticed one eye not opening as much as the other. If she has something in her eye blocking vision. I use the wet paper towel to dislodge it.
You may have to do the reptile-safe-water paper-towel-dunk-and-squeeze a few times. If you see your chameleon rolling their eyes under the skin of the eye, it's stretching and trying to get it to open more.
The first time I tried it, my female was hell bent on sprinting to safety. I held her, and I started to drop water on the "bad" eye. During the struggle I could see her moving her eye around, and the lids were closed. She stopped struggling long enough for her to notice I was helping, and the loathsome water wasn't a bad thing.
Every time she sees me spraying a paper towel she knows what I'm doing and sets herself up to feel safe, but, give me room to squeeze the paper towel over her eye (s).
If she stays with her eyes closed for any length of time she's allowing me to reload the paper towel with reptile safe water.
When Lady Jade is done, she's all "get the %#$@ away with that towel" and I know we're done for the day