I think you are handling her way too much. What exactly do you do when you clean out her cage? If you are removing plants just get her onto one and move the whole plant out. How often are you "cleaning?"
If she keeps falling you are really stressing her out - this is not good. You said you were afraid to grab her out of fear of hurting her - well, you are risking more damage with all these falls and stress. If she is hissing and biting she does NOT want to be held. The fact that she runs from and hides from you then turns and stays dark should be telling you something! When chams get scared they seem to tend to run with little care as to where they are going and busy looking back at their "predator" (in this case, you).
One other bit of advice...in case you have not learned this from the forum or the many articles and websites that we have suggested learn it now. Chameleons are very good at hiding symptoms of illness. Stress causes illness. You may find months from now that "something is wrong for no reason" yet it could very well be from the stress she is receiving now. So please do not handle her unless absolutely necessary. Dot is a little cutie and I, for one, would like to see you and her on this forum for a long time to come. I know they are adorable - especially as babies - but you took her in as your responsibility and her needs and wishes need to be respected 
lele
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0.1 veiled - Luna
0.2 felines - Kyndra and Líta
1.0 African Clawed Frog - Skipper
0.5 Mad. Hissers
0.1 Chilean Rose Hair Tarantula (no name yet)
?.? Goliath Bird-Eater Tarantula (no name yet)