Most times mosquitoes don't make us sick when they bite us. Also, there are groups of mosquitoes that, I think, only feed on humans and so may go extinct if they stop biting us. Also, a lion eating you will not make you sick. It will just make you dead. So, "No one will say, " I am sick...." " (Isaiah 33:24), is not an injunction against mosquitoes, or anything else, not biting us. What this is, is simply another example of a devout Christian taking a single line out of context from an ancient text and attempting to form a new doctrine. It is rather like the Appalachian snake handlers taking a single biblical passage and making it into a cult practice.
I read Isaiah 33. It proclaims many things, including the lame taking part in the pillage, and the blind receiving their fair portion of the pillage (Isaiah 33: 23), but your passage appears to make clear that it applies only to those living in Jerusalem.