My apologies for not replying earlier about the turtle drops. She said that giving the eye a cleaning with pure saline was more advisable then the turtle drops because it can be unpredictable what exactly is in the turtle drops depending on what brand and where you got them from.
Also, in this case we believe now that what caused the eye problem was a long tail mealybug infestation . We took his entire tank apart last night and scrubbed the hell out of it. There were mites buried in the farthest reaches of his pothos. We believe at this point that one of those things probably made a home in his eye socket which is what caused all the agitation. Cleaning with saline and lots of showers, combined with topical antibiotic eye drops has been working and his eye seems to be healing.
The biggest difference here is whether your cham has anything you can see in the socket. Yoshi had crusting in addition to keeping the eye closed and sunken. Also, the vet reasoned if it was just one eye and his behavior is the same (i.e. not lethargic or grouchy) it's less likely to be a nutrition/supplement issue - is Lizzie behaving normally?
This is just me, but if I were you I would get some pure saline and a foam makeup sponge (we used the wedge shaped ones) and give the eye a wipe with saline. Do not use Q tips because they can leave residue behind. Hopefully this helps. You might also consider trying to obtain a topical antibiotic drop in case of emergencies if your vet is far away - the one Yoshi was prescribed is Tobrex - I don't think it would be too hard to purchase online judging by the basic Google search I did. Mercifully our vet is literally across the street from us. Hopefully this helps.