Pet a cat that seemed docile&like an outdoor cat not stray. i bit my nails after i have no symptoms right now but should i be concerned about rabies?

Not particularly: Rabies is a regional issue & you can contact your local health department to see if there is any in your region to start with. Lack of a bite by a wild acting animal places your exposure on the minimal side of things. When you call your health department you can share your concern with them, since they usually control access to the vaccine. I doubt anyone would suggest it.