Kudos to Mom for being willing to take him to the vet but too bad she wouldn't go to Dr Boyer.
3 injections seems like a huge number of injections for such a small creature--and the deworming medicine is typically Pancur which can be given orally instead.
I'm not a vet but I'd be interested in another opinion before I had a 4 month old cham get 3 shots.
Did the vet do a fecal float?
If not, then why treat for worms?
Your supplementing and UVB have been good, so you would not expect a calcium deficiency.
Vitamin A deficiency can cause swollen eyelids but AFAIK, it would not cause anything to ooze from an eye--which is what I thought you said has happened.
You can easily treat a vitamin A deficiency at home (as has been mentioned in this thread before) but it is
extremely important to not give too much vitamin A.
A
very tiny drop of cod liver oil from cod liver oil capsules (the ones sold for people to take) can be put on the back of a feeder that you give to your cham and should correct the problem in one or 2 days.
Switch your multivitamin to Zoo Med's Reptivite without D3 . It contains the type of vitamin A that reptiles can actually use.
If that does not fix the eye problem, then perhaps you can convince your mom to get a second opinion from another vet who is known to be very knowledgeable about reptiles?
You can ask LLL Reptile in Menifee for a vet recommendation, since I couldn't imagine they wouldn't know some good ones.
Unless you can convince your Mom to take the longer drive, then you might need to look over the ARAV vets list and use the search feature to see if there are any reptile knowledgeable vets closer to you.
Here's the ARAV list
http://www.arav.org/find-a-vet/#California
A few more links
https://www.chameleonforums.com/veterinarian-resources-67/
Here are a few articles explaining why you need a reptile vet:
http://www.anapsid.org/vets/
http://www.veterinarypartner.com/Content.plx?A=1431&S=4
http://www.triciaswaterdragon.com/vetcare.htm