The Daily Mirror and their like have a lot to answer for.
The 90 days figure comes from the fact that SAGE have looked at the figures for re-infection with the virus that causes COVID and compared that with other coronaviruses. Chances of re-infection are very small, and they have found that this is the same for all the viruses they looked at. Re-infection with other coronaviruses sometimes happens after a year, very rarely within 6 months, and never within 3 months. So, they can say that re-infection with the COVID virus is not going to happen within 3 months, and not likely to happen within 6 months. Maybe after a year, maybe not.
This means we definitely won't need top-ups after 3 months, or probably even 6 months, but we might need it every year. But its really too early to say.
I really hope this doesn't put you off having the vaccine annsixty, the reports have spun this as negative when its actually positive. I couldn't find anything relevant on immunosuppression.