It might be a good idea to get the vaccine even if you've already had COVID. There's not been any CDC recommendations about it, but here's what they do say.

> There is not enough information currently available to say if or for how long after infection someone is protected from getting COVID-19 again; this is called natural immunity. Early evidence suggests natural immunity from COVID-19 may not last very long, but more studies are needed to better understand this. Until we have a vaccine available and the Advisory Committee on Immunization Practices makes recommendations to CDC on how to best use COVID-19 vaccines, CDC cannot comment on whether people who had COVID-19 should get a COVID-19 vaccine. [1]

Suffice it to say, I'll do whatever the CDC recommends. I've already had COVID, so I'm guessing I'll go last. But at the same time, I'll get the vaccine if it is recommended.

[1] https://www.cdc.gov/coronavirus/2019-ncov/vaccines/faq.html

Surely there is also not enough information on how long after vaccination someone is protected. This doesn't seem like a strong argument to me.

If infection with the actual virus doesn't confer immunity, I don't see much reason to think that the vaccine will work any better.

Everything I've read has suggested that people who've had COVID should still get the vaccine anyway, as it could act as a booster. And that, whether through natural immunity or a vaccine it looks likely that we'll need to get it 'topped up' after awhile.

Has there been medical advice anywhere that people who've had COVID don't need to get vaccinated?

The vaccine is still indicated for those who have had Covid.