> My DNA will be permanently altered and permanently create fake covid proteins ?
No, in fact, mechanisms in cells are in places so that "heteroduplexes" (meaning one filament of RNA and one of DNA paired together) are quickly degraded.
Secondly, the RNA doesn't even need to get to the nucleus, where the DNA is. All it needs is to land in the cytoplasm, where it will get processed by the protein synthesis machinery (ribosomes in primis) to produce the antigen. RNA in the cell isn't that stable as well, so it will be ultimately get degraded.