Cut finger on metal bed frame. had to stop bleeding, didn't wash until a short time after. last tetanus shot 3 yrs. ago. should i worry of infection?

Keep clean, watch.: Any cut can get infected, sometimes even if you take care of it properly. Your tetanus is up to date (if you've had the full series and boosters), so that;s not a germ to worry about. There are others. Clean with mild soap and water (half-strength), apply a light coat of bacitracin and a bandaid, twice a day & watch for signs of infection: marked redness, pus, increased pain, etc, see doc then.