the mRNA vaccines are new, but the way they work seems like there should be little residual concerns. You get an injection of specific instructions, something your body already creates for other purposes. Once the mRNA has been delivered, it is destroyed. Then your body builds part of the spike protein, which are harmless themselves, but your immune system recognizes them and destroys them, so anything related to the vaccine and proteins should be gone pretty quickly.
mRNA vaccines have been tested for other viruses before COVID, so there should be some knowledge any longer term concerns.