So sorry that you've found yourself here.
Many women miscarry without complication at home. D&C is recommended by some doctors for it's speed and relative physical ease, but not necessary unless a) your body does not take care of things and you begin to get an infection (this would take many weeks generally) b) your body takes care of it but it's not complete or c) you begin to bleed too heavily, more than a pad every 30-60 minutes continued.
Honestly, if you go to the ER and are not in an emergent situation they will likely give you pain meds and send you home, but if you begin to feel that you are not able to continue without help then do go in since they can at least ease pain.
Many of us here have miscarried at home, so feel free to ask questions if you have any.
ETA: make sure you follow up with your doc to confirm miscarriage and confirm that everything has passed. Occasionally remnants are left and, if not removed, can cause infection.