I think you took the first right steps, which is that you removed the foreign object and you washed out the area well. This will often be all that is required to prevent an infection.
However, you still need to go see your doctor
. This is because the one thing that washing out and disinfection might not help prevent is tetanus, which you are at risk of getting if your tetanus shot is not up to date. Your doctor will be able to review your immunization record to see if you need to get another tetanus shot to cover you for this.
Otherwise, you can continue to provide routine care to the injured area, meaning cover it with a bandage and apply antibacterial ointment. If you start to notice that the skin around the injured area is becoming very red and warm, or if you notice any pus or drainage coming out of the wound, then these might be signs that the area is getting infected. In this case, you should also see your doctor, as sometimes these injuries need to be treated with oral antibiotics in order to help get the infection under control.