What happens if you don't get a Tetanus shot after getting cut with rusty metal?

Tetanus is an anaerobic bacteria- it can’t survive in an oxygenated environment. The risk of tetanus is wildly exaggerated in society, just like the risk of quicksand and alien abduction. Tetanus is normally found in manure or in dirt, and not often on rusty metal and rarely on clean metal. The only reason to worry (unless you’re really unlucky) would be a deep puncture wound that had tetanus present AND didn’t bleed

In this case you must clean the wound liberally with soap (or other disinfectants)

If you’re still in doubt you could get the TIG shot which is a tetanus immunoglobin, which is an anti-toxin

The tig shot is not a vaccine, which people always try to get after suspected tetanus exposure. You do not need a tetanus vaccine if you suspect tetanus exposure:
-it is impossible to vaccinate against a bacterial infection after the exposure
-it takes weeks for you to develop immune response to tetanus after the vaccine, assuming the vaccine is successful
-You can take tetanus containing vaccines either TT or Td or dTap vaccine; there’s a good chance you’ve had this vaccine already