If i just had covid, am i immune from every variant for now or just the one i had?

Physicians have seen patients that are vaccinated/boostered and who have had SARS Covid-19 on more than one occasion. Difference is that re-infection is usually much less virulent. Almost all Covid deaths and Covid hospitalizations, since Vaccine availability, has been among the unvaccinated. Add natural immunity (Covid infection) to vaccines, and reinfection will have only very mild symptoms

The Covid-19 variants are only different in the spikes but not the core (envelope and RNA). With natural immunity, you can still be infected with the new variant because the virus uses different spikes for entering the cells but viral replication is mostly inhibited because you have antibodies to the core components so the disease with reinfection is very mild or likely asymptomatic.