The captchas do suck. If I have any confusion about any of the characters, I just type xx and go to the next one, and repeat as needed until I get one that’s legible.
Doctor is wrong about prescribing. They can basically prescribe anything for anything, within ethical boundaries. A lot of medications are used “off-label;” it’s very common. Anticonvulsants are commonly used off-label to treat neuropathic pain, for example. Insurance probably won’t pay for off-label meds, but HCQ is cheap so no biggie.