Sounds like you are working to really ensure that you have proper care (husbandry) for your cham. I know how attached you can get to them.
Shedding is usually one of the main reasons for "eye rubbing". I notice my juvinile cham (8 months) old doing it prior and during shed. Occasionally the will become a little swollen.
You can purchase an ointment call "terramycin" over the counter. As my breeder put it..."its a must have for every reptile owner". I have used this with good results.
The humidity is important to assist with shed and for overall health. A lot of us folks shower our chams every 2 - 3 weeks. I have attached some fake vines in the shower, then run it fairly warm so that the water bounces up and the humidity gets high, usually for 20-30 minutes. You can also use plastic sheeting on the outside of the enclosure (make sure that you still have adequate air flow) to help increase the humidity inside the cage. Of course, natural foliage helps with this as well. Rememember that the air-con and heater take humidity out of the air.
As for the gut load, leafy greens, oranges, strawberrys and whole grains are great crix food. There are several links above that will get you direct information on this.
Good Luck.
Kris
Here are my shed pics..the most recent in July, and then his second shed as a baby, and his very first shed (looks like baggy clothes LOL)



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2.1 Black Labs Tucker, Raider and Lacey
1.0 Lepoard Gecko Kumar (Another lost pet RIP and party on with Harold!)
2.0 Horses Smoothie and Rocky
1.0 Husbands (he puts up with me)
1.2 Kids-Trevor (congrats c/o 2006), Logan and Rylie
1.1 Ferrets Tank and Ellie (The fun fuzzies)
1.1 Veiled Chams Squiggy and Pudge (may she RIP)
0.1 Snowflake Cornsnake Lucky